Short answer: you get the rights to view a copy of the book using a particular piece of technology.
This is the real sore point of eBook (that applies to all digital media such as movies, music, and games): often DRM does not allow you to migrate your books from one system to any other.
Amazon, for example, offers their reader on many platforms so you can read your Kindle books, for example, on an Android tablet.
But you are still chained to Amazon for your books.
The same, if not worst, apply to all others.
In theory you should be able to read the books you purchased on all readers supporting the same DRM of your books, however this is far from user friendly and not encouraged by the content owners.
One option is buy eBooks from more "liberal" sources (some companies have less restrictive DRM systems) and import those books in the reader you happen to use.
Ideally we should have a common DRM framework that all content owners and distributors must use, so that you can legally read the book you bought on any device you like.
Unfortunately this is not happening anywhere, and the "locked silos" system initiated by Apple is now copied by all... with the consumers as the main losers in the process.
Obviously you can't re-sell second hand eBooks, and you cannot borrow one like you could do with a paper version.
I love the flexibility of reading eBooks but I hate the rigidity of their business model.