They have opened their own Android App Store. It's going to be competing with Google's own Android Market, but Amazon has a few features that Google's Market doesn't.
First of all, Amazon's new store is going to be a bit more strict on what types of Apps it sells. Currently, Google relies on customer reviews and flags to determine if an App is offensive or something else that shouldn't be there. Amazon, however, will take a stance a bit more like Apple has with their App Store and will review every piece of software that is available on the store and if it feels that something shouldn't be sold, it won't be sold.
Second, Amazon's store will support devices that aren't currently supported by Google's Market. From what I've been able to determine, there is some sort of cooperative that has been set up by Google and many manufacturers are a part of it. If a company is a part of it, then their device is officially supported by the Market...however, if a company is using the Android OS but isn't part of the co-op, then they have no official support for Google's Market. This is the case with my Archos A70. It is not officially supported by Google so the Market doesn't work correctly on it. There are ways around this, however, with a hacked Market Fix or owning an Android powered phone and connecting both devices to the same account. However, neither of those is really an ideal solution, so Amazon has gone around it completely by just saying that ANY Android powered device will be fully supported by the Amazon App Store. That's a cool feature that makes my tablet seem much easier to use.
Third, Amazon will be giving away one free app that normally costs something every single day. Today, the initial launch day, they are giving away "Angry Birds Rio" for free. Sure, it normally only costs 99 cents, but anything that's free is cool. Especially when it's such a popular game like "Angry Birds." Amazon says that every day there will be a new free app, so it's definitely worth checking everyday to see if it's something you're interested in.
Overall, I think that Amazon may have just become my vendor of choice for Apps for my two Android powered devices. I look forward to seeing how this all goes.