Database technology is perhaps the one area of computing that remains somewhat specialized. The domain of the DBA (database administrator) is still seen as being complex and rarefied. However, this is changing as many DBAs now commonly manage more than 20 different databases.
The advent of Derby opens up the database field to the ordinary programmer among whose number I include myself. Not only can you use Derby to learn about embedded database engines, you can also dive into the network server end of databases. The latter has traditionally always resided inside the data center, but now we can all try it on for size.
So, if you want to learn databases in depth, a good place to start is with the embedded framework. When you're comfortable with that area, you can move into the network server end—i.e., the high end of the spectrum. Naturally, to use databases effectively you also have to learn about data modelling, SQL, relational issues, and more. I haven't covered these but there are many excellent books on these topics.