The point where two things split off from each other is called a divergence. When you're walking in the woods and face a divergence in the path, you have to make a choice about which way to go.
A divergence doesn't have to be a physical split — it can also be a philosophical division. The divergence of opinion between a school board and a group of parents might cause such a heated argument that the students at the meeting are obviously better behaved than the adults. Divergence can also mean a deviation from standards or norms, like the divergence between your state's smoking laws and those of your neighboring states.