Update: If you're running iOS 7 or higher, you'll want to check out the new way to fully close your background applications.
With the newest version of iPhone firmware, you will be able to multitask. Finally, Apple has given us the ability to access more than one program at once and enjoy our Apps to the fullest. By closing an app the way you would on a 3G phone (clicking the home button), you will no longer fully quit an app. This is similar to the way things work on a Mac OS - clicking the "X" won't actually quit a program on a Mac until you actually go to "Quit" in the drop-down menu.
With this new feature, some might be confused on how to actually shut down their running apps, instead of leaving them on in the background. If you're confused as to how to sign out of apps and save speed and battery life, check out this clip. The process is actually quite easy once you get the hang of it.