App Stores provide a convenient method for users to find and buy software and games. Technically speaking, Linux had these in the form of package repositories for ages, although without the commercial aspect.
Currently the most known app store for Linux is the Ubuntu Software Center. When it comes to games, Steam and Desura are distribution agnostic software store (although officially Steam only supports Ubuntu currently), and Gameolith packages the games for you.
And obviously any web-based digital distribution platform can be used as an app store, although most users expect some benefits from app stores like automatic updates and having their purchases in one convenient place from where they can redownload them. An indie oriented web-based service for selling games that provides an app store-like interface is Indievania.