When you talk about the genesis of something, you're talking about where it began. The genesis of hip-hop music was the party scene in New York City’s South Bronx in the 1970s.
The Jewish Torah and the Christian Scriptures begin with the book of Genesis, which describes God separating light from darkness and creating the universe. Genesis is the very start of something, its birth. But you probably wouldn't refer to your own birth as a genesis. When you describe something as a genesis, you're usually referring to the beginning of a movement or an idea.