First and foremost, Amazon is promising to give away one paid app for free every day. Today it's Angry Birds Rio, and it only retails for 99 cents, but that doesn't really matter: people love free stuff. People will download stuff simply because it's free, even if they don't want it! The best bit (or worst bit) is that developers still get 20% of the usual retail price, which will be paid out of Amazon's pockets.
The next defining feature is Amazon Appstore exclusives. Angry Birds Rio, CoD:MW:Force Recon and other apps will be available only from Amazon. As we know from the console wars, exclusive titles aren't always a good thing, but who cares? Amazon simply wants unique selling points, and exclusive titles are definitely that.
It's not all good, though. We ran in to some rather serious bugs while playing around with the Amazon Appstore for Android app, and then there's the matter of having to enable installation from Unknown Sources before it will even install...
Gallery: Amazon Appstore for Android