The complex retroviral enzymes in the spider's venom that were transferred at the time of the bite triggered a profound and significant change in the genetic expression of Peter Parker's entire body. The retrovirus contained the codes for certain spider traits that were inserted into Peter's DNA. It transformed the way his body systems work, including his glands, nerves, and muscles. Spider-Man possesses superhuman strength, reflexes, and equilibrium; the ability to stick with great tenacity to most surfaces via microscopic claws located on his hands and feet; a subconscious premonitional danger sense; and an ability to project an organic webbing in a manner similar to that of spiders.
Peter's physical structure has been altered and enhanced to superhuman proportions. His overall metabolic efficiency has been increased, allowing him to fuel superhuman muscles, far stronger and denser than any normal human being. The origins of Spider-Man's strength is in the webs. Spider webbing is a protein-based fiber, some types of which are stronger than steel. Human muscles are also protein-based fibers so, by chance the rewriting of Parker's DNA led to his already present muscle protein structure being rewritten to be more like spider webbing so his human muscles gained titanic strength. His body also now produces more of the contractile proteins of muscles, actin and myosin. More contractile protein, further his enhances his musculature strength. With his musculature altered as it is, Spider-Man is capable of lifting over ten tons under optimal conditions and at maximum exertion, in both a leg press or a bench press.
The make-up of his skeleton has also been augmented to support these weights, so that he doesn't snap in half when lifting a car over his head. With this degree of strength, Spider-Man can easily punch through thin layers of carbon steel, sustaining only minimal damage to his tissues -- roughly similar to a normal person punching through a sheetrock wall. His stamina has also been augmented to slightly enhanced levels, however, on a proportional level, he is roughly same to the average person, lifting 300 lbs is extremely difficult, and an act difficult to sustain. Spider-Man is no different, except that his maximum is roughly 10 tons. His strength is more than sufficient enough to propel himself to impressive leaps and bounds or feats of overall agility, especially when combined with his insubstantial mass.
Speed is directly related to the strength of muscle. As good a shape as he's in, a powerless Spider-Man can bench a fair bit more than his own 165 lb weight, he could bench 200 lbs without his powers. His powers make him 100 times stronger. And increasing the energy/strength available increases the speed by the square root of that figure. Therefore his powers only make him 10 times faster. Which given even the average for his physical acuity, puts him at approximately 100 miles per hour for short sprints. He can run at over 45 mph quite a while at his peak ability.
Spider-Man has reflexes 15 times faster than normal humans. He has enhanced energy resources for his strength and those higher energies manifest all the way down to his metabolic intracellular processes, the nerve conduction velocity of his nervous system is faster simply by sheer brute energy resources. Spider-Man is able to respond to stimulus in a virtually instantaneous manner. He is frequently able to dodge automatic gunfire from multiple sources provided he has some distance between himself and the source, and is able to move with enough room to generate necessary momentum.
Spider-Man is capable of incredible feats of superhuman agility. Agility is not so much an attribute as it is a combination of attributes, many of which Spider-Man has at vast levels. His super-strength and speed allow him to do the necessary movements. The fact that his "web based" tissues have much higher elasticity despite their strength gives him amazing flexibility. His superhuman reflexes help him adapt to any changing environment with vast rapidity. They also allow him to find equilibrium almost instantly in any given situation. This enhanced nerve efficiency is also applied to his cerebellum, allowing him superhuman coordination and aiding his balance. Also an increase in proprioreceptors and an increase in their sensitivity aids his coordination and balance even more so. His stamina with movement is similarly enhanced, and he can keep himself moving quickly for nearly an entire day. This agility is augmented and enhanced by the spider-sense, rendering him even more capable of feats of miraculous evasion. All these things combined give Spider-Man super-agility.
Spider-Man's entire body has been made somewhat more resilient. His web-like tissues are very tough, especially since they're woven into the meshes of his body. This gives him a great deal of shock absorbing capability and general resilience. In effect, his skin and muscles seem 'thicker', and his bones are more resistant to breaking. Nothing akin to Kevlar, however a needle will have a bit of trouble breaking the skin, for example, but a sword will be more than sufficient for the job. Overall, his body is simply hardier. His bones are stronger, partly to support the tremendous weights he is capable of lifting. His skin is tougher, to reduce the impact of blows, but a powerful punch can still leave him reeling, even from one who is merely an exceptionally strong human. He's far from invulnerable, but it's enough to take the edge of off many injuries enough to keep him going, or save him from the absolute brink of death on many occasions.
The sheer hardiness and efficiency of Spider-Man's body grants enhanced health, he tends to heal at an accelerated rate, and he's seemingly resilient to poison and disease. His aging is slightly retarded as well. Bruises and small cuts vanish within a few days. Broken bones also heal faster, probably 2 to 3 times faster than an average human, as do larger wounds. However, his rate of healing is not so dramatic as to not require such things as disinfectant, bandages, stitches, and the like. Gunshots are still gunshots, for example, and even one is going to take Spider-Man out of action for some time a number of days, perhaps over a week. Spider-Man's accelerated healing is not quite dramatic enough to make most people question the speed in which Peter's cuts and bruises vanish, unless they were extremely careful to keep tabs on his status.
Spider-Man can stick to surfaces. He sticks to things using retractable microscopic hairs on the bottom of his fingertips and the soles of his feet. The hairs retract hydraulically in a similar manner to how spider legs work. These hairs are so small that they create electrostatic connections to interact with surfaces on a molecular level. They get very close to the atom surfaces and actually develop forces from atomic to atomic interaction, so they are really sticking in between the atomic structure and getting the atoms close enough to each other that they form temporary molecular bonds between Peter's body and another object. This enables Spider-Man to cling to solid surfaces with vast force and scale walls simply by placing his hands on them.
The most incredible of all of Spider-Man's many superhuman attributes is his 'spidey-sense' or 'spider-sense' that warns him of impending danger through a tingling sensation in the back of his skull and upper neck. The secrets of Spider-Man's spider-sense lie within three factors, electro/magnetoreception, extreme sensitivity to atmospheric vibrations, and super-fast reflexes. Parker's entire dermis acts as a sensor that uses ambient energy to see through objects, almost like omnidirectional x-ray vision. Since this is too much information for the normal human consciousness to process, his subconscious does the work and only alerts the conscious mind to things of importance.
Spider-Man can't be snuck up on because of the omnidirectional "sight" of his sense, it always alerts him which direction danger comes from. Weapons (guns, knives, brass knuckles, etc.) have their own distinct reflective signatures from ambient energy due to their shapes and compositions, so spider-sense would pick them up within range and warn Spider-Man, whether they were hidden or not.
Everyone also has their own unique biochemically generated electromagnetic aura. Spider-Man's subconscious can use the spider-sense to see the EM aura of a super-villain in costume and remember it, and then if it happens to encounter the same aura surrounding a civilian, it will warn Spider-Man that the person was the villain out of costume by simply giving him "a bad feeling" about that person. This also allows Parker to spot people (villains) in disguise. It also allows him to sense people in hiding.
Spider-sense also acts as radar due to its omnidirectional nature, allowing Spider-Man to sense his surroundings even when he's blinded or in total darkness, because there's always some form of radiation present. Spider-sense warns Spider-Man if he's about to step on a creaky floorboard when he's trying to be quiet. This works because his subconscious knows he doesn't want to make noise and is scanning for any way he might, this includes sensing if the structural integrity of the board he's about to step on isn't as sound as the one he just quietly stepped on.
Spider-Man knows when he's being watched too, so he doesn't accidentally change in front of someone he doesn't want to know his secret. With spider-sense constantly "x-ray viewing" in all directions, it knows when he's being looked at because it can see the looker and warns him accordingly. This same reason is how he knows he's being aimed at with a weapon, his sense is literally "looking down the barrel".
When disarming a bomb, his subconscious using his spider-sense scans the entire design of the bomb, including which wires current is flowing through and using Parker's affinity for science, figures out which wires to cut, then alerts him accordingly. Its omni x-raying abilities also warn him of what he would consider a potential danger even on the other side of a wall or door.
His spider-sense is also able to alert him to the hostile attitudes of people due to the changes in EM aura that occur with changes in emotional states.
A supreme dermal sensitivity to vibrations aids the EM aspect, allowing movement to be felt from quite a distance. This combined with his ultra-fast reflexes kicking in instinctively, makes his spider-sense possible.
Sphincter like sacks that produce chemical known as 'web fluid' have formed on Spider-Man's wrists. The super-strong sphincter muscles can propel the fluid at high speeds. The fluid comes out very tiny, but absorbs a lot of air causing it to expand in size and length and it uses that "oxidizing" effect to increase its strength to form a long-chain polymer knit of extremely tough but flexible, elastic fiber. That way, Spider-Man can have "a lot of it" without really having to produce a lot of it. In addition the compound uses carbon out of airborne carbon dioxide to knit itself into webs, which allows for vast strength. The actual web is analogous to nylon with the tensile strength of Kevlar, naturally weaving it into a rope-like shape. The adhesive quality of the substances decreases rapidly with exposure to air; therefore, the ends, where it quickly strikes the surface it is meant to stick to, stick extremely well, whereas the actual length of web, which remains exposed to air, is more easily handled. This trait is critical to most of it's functions, including the creation of complex webs, hardened surfaces, and so forth.
The compound continues to absorb elements from the air after forming, and eventually gets to the point of super-saturation and keeps absorbing till it crumbles, all in a process that takes about two hours. It dissolves into a non-toxic powder.
Spider-Man is extremely talented with the usage of these webs by virtue of natural talent and constant practice since he became a superhero. He is capable of targeting a line or glob with bulls eye accuracy, even at the longer ranges allowed by his web-shooters, or firing at moving targets. He has used this ability frequently to strike guns from the hands of multiple foes with extreme speed, before a single one of them could get a shot off. He can quickly form a variety of complicated shapes and forms, like sheets of web, larger structures, and so forth. His reaction speed is extremely high due to his natural reflexes.
Naturally, Spider-Man is infamous for using his webs to swing through the cityscape of New York, to the point where he can very accurately simulate flight. He can swing with great speeds, crossing boroughs far faster than any normal person could using the Subway, or a car. He's quite agile in the air, perhaps even more so than he is on the ground, and is naturally even more difficult to hit. He is adept at identifying the best places to attach a web line for swinging, and can easily navigate highly stressful situations, easily keeping up and sometimes outmaneuvering a flight-capable individual. He is able to perform a variety of other stunts, like forming a slingshot to launch himself even further than he normally could, or saving himself from an otherwise deadly fall, either by quickly creating a trampoline to catch himself, or by attaching a web line to something else mere moments before falling.