I've got involved in a project with entity manager in it. It's a bit unclear why should one use it. We have databases to store information in if we don't we can use classes to store informations in without the entity manager. The question is is it worth the effort to learn? Is it a widely used tool?
I know it's a bit opinion based but I'm interested in the facts mainly. But usually others experience shows how good a tool is.
Yes, JPA and Hibernate are widely used. Their benefits are the speed of the development (especially on the early stages of the project), but since it's a very complicated technology not everyone gets to use it effectively.
Ultimately knowing JDBC and databases is much more important than knowing ORMs. Mostly because everything else related to DBs in Java (including ORMs) is based on JDBC. But also if you need to write a very performant code - JDBC could be the right level of abstraction for you.
If you want to learn ORMs I'd advise to start with the book POJOs In Action - it explains the fundamental principles behind these frameworks. And after that check out Java Persistence with Hibernate - this one is more technically involved and describes all sorts of features in Hibernate.
Apart from the fully-featured ORMs there are lighter technologies that ease up the low-level JDBC burden: jOOQ, Spring JDBC, MyBatis.