is there any way to browse available Adobe Digital Editions books? I would like to download some but do not exactly know what I am looking for and some sort of a library would be good.
ADE is not a library, it is software to allow a person to read ebooks. Here are sources for free ebooks if that's what you want:
Many distributors use Adobe DRM to secure their books. Some of the best known include: B&N, Sony, Kobo, and Overdrive. But all have their own branded reading system that the user uses for opening these files.
Typically, some books use encryption (known as DRM) to protect its books. Adobe DE allows the reader to view ebooks with DRM if the publisher or distributor includes this particular DRM.
As it happens, many distributors, rather than sell you this DRMed file, just build their own reading system which incorporates in some way Adobe DE. Typically it does not make sense for publishers to sell you an encrypted file because they expect you to read it in a special app (like Overdrive, Nook, Kobo, etc).
The reason publishers don't typically do this is that they would need to purchase a special server to distribute Adobe DE files. From the FAQ:
Adobe offers a content protection service, Adobe Content Server. Adobe Content Server is a robust server solution that digitally protects PDF and reflowable EPUB content for Adobe Digital Editions and supported mobile devices. Easy to integrate into existing systems using industry standard technologies, Content Server allows you to host, manage, and deliver files from your existing infrastructure to Digital Editions users.
Truthfully, publishers would prefer to work through a distributor's reading app than encrypt the file themselves and sell it directly to the consumer. It can be somewhat confusing for users to open and read stuff in Adobe DE.
Adobe DE can also read unencrypted PDFs and epub files, and that is the primary way people use it. I'm a publisher, and I find it useful for testing ebook files that I create. Occasionally a publisher will send a file which can only be readable in an app which accepts Adobe DRM, but that is only if the publisher runs the Adobe Content server.