Also, they seem to have different prices than what's on the official Market. e.g. Angry Birds is free on Android Market but costs $0.99 on Amazon Appstore.
In this instance, it's because the version from Amazon doesn't have ads. Not sure if that's the case for anything else though.
Couple other notes... you have to be able to enable app installation from Unknown Sources (Settings->Application->Unknown Sources) to not only install their store but also the apps you get from them. Some carriers remove this or force it to disabled; hence all the messages about it not being supported on AT&T.
Also, I believe Amazon requires all apps in their store use their DRM and for an app to authorize your use it needs to communicate with the Appstore app. Thus, while you can install the Appstore app on multiple devices and use your apps on all of them, your apps may quit working if you uninstall the Appstore.
Isn't it great living in this country-limited, carrier-restricted, DRM-ed world?