Genetic memory in Battlestar Galactica is the reason the culture of the Colonial humans in the reimagined series is aesthetically identical to 'our' culture.
In the reimagined Battlestar Galactica series, humans naturally evolved on two planets: our Earth and Kobol. Kobol-evolved humans possess a capacity for genetic memory. This genetic memory does not take the form of passing on personal memories, but the passing on of an unconscious knowledge of certain invented concepts and ideas such as technology, language, engineering and even fashion and music along with various other aesthetic cultural aspects.
In terms of culture, humans on Kobol were just like the Twelve Colonies at the time of the attack - aesthetically identical to the early 21st century Western world. After the exodus to the colonies, humanity lost these aspects. However, over a period of a couple thousand years, they completely reconstituted because the genetic memory of these concepts and ideas 'leaked' into the subconscious minds of various people who gradually and collectively reinvented these aspects of Kobol society. Eventually, even the genetic memory of the concept of artificial life in the form of Cylons was reconstituted in the conscious minds of such men as Daniel Graystone and Tomas Vergis.
When the Kobol-evolved human Colonials settled our Earth and interbred with Earth-evolved humans, the genetic memory capacity was diluted and became latent. It took more than 140,000 years before it became active again. After the end of the Stone Age, the capacity began to reemerge and certain ideas and concepts reemerged. However, they reappeared only in rudimentary, fragmented and even modified forms. For example, the Colonial religion gradually reconstituted in the minds of the people of ancient Greece - but in a modified form (e.g. the "Lords of Kobol" became the "Gods of Olympus).
Over a period of several millennia, a multitude of Colonial ideas, concepts, and cultural aspects reemerged because of genetic memory. Although they would continue to reemerge in rudimentary, modified and fragmented forms, eventually these fragments coalesced into complete reconstitution of Colonial aspects. For example, the Colonial language eventually reconstituted as the "English" language. The English language did not suddenly appear, but instead evolved through centuries of modifications along with amalgamations from numerous other languages. It was all the result of the genetic memory of the language 'leaking' into the subconscious minds of people who unconsciously directed the language toward a linguistic endpoint that is an exact replication of the Colonial language (however, the profanity word "frak" remained modified from its original form).
As a result of genetic memory, by the early 21st century virtually every cultural aspect of Colonial society has reemerged: language, names, fashion, engineering, architecture, furniture, music, art, cuisine, household appliances, television, automobiles, federalized government, judicial systems, labor unions, military protocols, etc. Countries such as the United States, Canada, and the United Kingdom collectively form a near perfect replication of the society of the Twelve Colonies of Kobol more than 150,000 years ago – just without advanced technology such as jump drive and sentient machines...yet.