WHAT IS APK FILE
APK is short for Android Package Kit, is the package file used by the Android operating system for distribution and installation of apps (and games of course). Basically it is a zip-file, and you can see its contents simply by unpacking.
Anyway APK is a package for Android and you install games from it. The system does. And this is precisely what is going on when you reach a Play Store for another game: the phone downloads the apk file and installs it, and that's called a "trusted source". However - you can significantly extend your smartphone experience and get these apk files by very other means, downloading it straight from a developer for example or from an alternative store, like Amazon appstore or GetJar, whatever.