Here's my understanding of how it works:
-Unless an app is actively working (streaming, downloading, etc.) and using a process actively, Android does not just keep it running like it would on a PC. It "saves the state" of the app in the cache/memory so that you can resume it later as if it had never been closed.
-When you long press the home button you get a list of "recent apps" and you can reopen those with the saved state.
-Apps that are currently running and using processes actively should be listed under task manager (bottom left button when you long press home).
-Clearing apps from the recent apps list removes their saved state from the cache. I've read that this is not actually necessary as Android will automatically start removing them on its own should it run low on memory and need to do a little housekeeping.