An "app store" (the very name is litigious; Apple is trying to claim it as a trademark) is a marketplace for applications, typically for smartphones. Apple championed the idea of software retailing ecosystems as an evolution of iTunes. The iPhone is now nearly half of Apple's revenue, and the very largest part of applications for the iPhones come through the iTunes store as a distribution channel. Apple makes a commission from each application, as does Google and Amazon.
Inside an app store -- let's take Apple's, for example -- is a repository of applications divided into categories and "Top 25" selections. Apps can be free, often sponsored by ads, or paid versions which generally are bereft of ads. You'll need some kind of logon to obtain software -- but ultimately you don't need to sign up with a credit card or credit source until you actually buy something. Other apps ask for donations, or are just plain free, as in beer. Developers ought to be able to determine the sales model they like: paid, subsidized by advertising, or here-ya-go-free. Amazon doesn't quite do that.
Amazon wants the applications you buy to be successful. For Amazon. Before a developer even "signs up" for the AppStore, they must submit to great fealty: