The Amazon Appstore for Android is an online marketplace that caters to Amazon's tablets and phones but is usable by anyone with an Android device.
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Pro Amazon Underground
"Actually free" apps with free in-app purchases. This only applies to a selection of older apps with the "actually free" banner, not to everything.
Pro Curated selection of apps
Unlike the Google Play Store where anyone can publish anything they like, the Amazon Appstore has a review process before an app is allowed to be published to the store. This means everything is curated and supposedly is guaranteed to work as well as safe to use.
The Amazon Appstore gets exclusives from time to time such as The Wolf Among Us or République. Though some of the exclusives are also tied to their own hardware such as the HDX. Not only is this a good incentive to purchase Amazon Android devices, but it also shows a commitment to feature hardcore games on their app store.
Pro Amazon developer services
Amazon offers app publishing to their users along with tools to pre-test their apps for compatibility. This allows for easy access to publishers in order to get their apps n the store.
Pro Sideloads on any Android device
It's not just for Kindle.
Using the Amazon Appstore is pretty convenient as a very large portion of the population already have an Amazon account from using their normal website for ordering goods. Also the fact that they allow anyone to install the store onto their devices means the users collection of apps can be installed easily.
Con Apps can not be used if store is uninstalled
Any app installed from the Amazon Appstore will not work if the Amazon Appstore itself is uninstalled. this is basically a DRM system where in any app from the store will not work if the store is not installed.
Con Less apps than Google Play Store
There are far less apps on the Amazon Appstore than the Google Play Store. The apps that are available on Amazon are also slower to get updates, in part due to the store not being as popular as well as the verification process Amazon uses to insure the apps are of quality and are not spyware.