JPA was born as the acronym for Java Persistence API. When Java EE was donated to the Eclipse Foundation under the Jakarta EE project, the name of the API changed to Jakarta Persistence but the term JPA is still in use. JPA solves the object-relational impedance mismatch by allowing you to map Java objects to database tables and is one of the most (if not the most) used persistence frameworks for Java.
JPA is an API specification that someone can implement–JPA providers or implementations. The most popular JPA implementation is Hibernate ORM. You can use Hibernate ORM without JPA or through JPA. One potential advantage of using it with JPA is that you can move between implementations if you want (something I have never seen happening, though). Another advantage is that someone with experience in, say EclipseLink or Apache OpenJPA, then they can use at least part of that experience when moving to Hibernate.