Like the iPhone, BlackBerry, PC, and Mac versions that came before it, the app allows you to read books purchased from Amazon's Kindle Store (which currently stocks a whopping 600,000-plus titles). You can also read a sample first chapter of just about any book in the catalog.
If you already own a Kindle, the app will sync all your books and bookmarks, keeping track of the last page you read on either device and jumping to that page wherever you access the book next.
However, Kindle ownership is not at all necessary. Your phone serves as the e-book viewer; the app connects you to the bookstore.
A lot of people balk at the idea of reading books on a small(ish), electronic screen, especially one that's backlit. My advice: don't knock it till you've tried. I've been an e-book reader for years, and I don't experience eyestrain, headaches, or any such ill effects.
What I do get is the convenience of having a good book in my pocket everywhere I go. I also get to read in bed at night without disturbing the missus.
Kindle for Android is free -- get it by searching for "Kindle" in the Android Market on your phone. Then hit the comments and answer this question: read any good e-books lately? One I can't recommend highly enough: This is Where I Leave You, by Jonathan Tropper.