This is a huge part of Android that, IMO, doesn't get enough press. On the iPhone, an "app" is a silo. You run it, it takes over, you go back to the home screen, it stops (modulo some limited background processing in iOS 4).

On Android, an "app" can be seamlessly integrated into the entire system. Think "extension" in classic Mac OS. My first experience with this in Android was "Rings Extended," one of the first apps in the market. It can (at your option) COMPLETELY REPLACE the ringtone selector, system-wide. Other "apps" can completely replace the home screen (OpenHome, aHome were two early examples). Other "apps" can complete replace the system-wide keyboard.

[disclaimer: I work for Google but not on Android stuff. My experience on Android is 100% based on phones my employer gave me for free.]