A Spawn Core is almost exactly what it is named. A Spawn Core is the central source of Spawn Intelligence and new units. With a Core around, the Spawn units are much more intelligent, and powerful.
Although a Core's main purpose is to produce new units, it does so on a scale much greater than that of its younger Queen brethren. It also makes nearby units more powerful and the presense of a Spawn Core can strengthen a Spawn infestation's grip on a Planet or multiple Planets. A Swarm of Spawn Cores destroyed an entire race known as the Havonians.
Cores are massive, they resemble massive Squid beings with large gaping maws and hundreds of tentacles. Sprouted out of the ground they can grow to heights as large as 4,000 feet, as tall as a Haven's Apex and are technically living buildings. A Spawn Core, if inside of a structure such as a Zodiac World Breaker, could grow to consume and eventually become the structure. The most terrifying thing about a Spawn Core is that they have no critical mass, they can keep growing and consuming and pumping out more Seed Spawn, and if they have opened a portal inside of them they will be nearly immortal, vulnerable to none other than The Eye.