When I build an app on ipad, if I close the app and restart it like you do for any other app within the ipad, it actually wasn't closed at all and runs in the background.
What do I need to do to close it properly? I do not want it to run as a background task? What settings can prevent that?
The Editor's Player Settings -> Settings for iOS -> Other Settings has a Configuration area with a checkbox for "Exit on Suspend". Check it and build, then the home button will cause your application to exit. I'm running Unity Version 3.2.0f4.
Apps do not run in the background anyway (aside from specific services, which aren't usable directly in Unity). You really don't need to manage this; the OS does it for you. The "multitasking" in iOS is for the most part just task switching.