JPA is an API, one which Hibernate implements.Hibernate predates JPA. Before JPA, you write native hibernate code to do your ORM. JPA is just the interface, so now you write JPA code and you need to find an implementation. Hibernate happens to be an implementation.
So your choices are this:
hibernate, toplink, etc...
The advantage to JPA is that it allows you to swap out your implementation if need be. The disadvantage is that the native hibernate/toplink/etc... API may offer functionality that the JPA specification doesn't support.