It’s helpful to know how to truly quit an app on an iPhone, iPad or iPod Touch. Some times apps stop working properly. When this occurs you can force the app to quit or close. In iOS version 7 and higher, here’s how to force an app to quit:

• Rapidly press the Home button twice in a row. The Home button is the round button on the lower part of the face of the iPhone.
• You’re iPhone switches to a mode that lets you swipe from left to right to see each of the apps that is open. When you’re looking at the screen for the app that you want to quit, swipe up. If you close all apps then you’ll only see the Home screen when you try to swipe from left to right.
• When you’re done quitting apps then press the Home button again to get out of this mode.
• Tap on the misbehaving app’s icon to open it and see if it now works properly.
• If your app continues to misbehave then I recommend restarting your device.

Apple has an article which describes this same process and will be updated more often than this web page if the process changes over time.

On a related note, a widely-held misconception is that the applications listed in the multitasking bar are using some of your device’s memory and processor, thus slowing it down. This isn’t exactly correct. Read this excellent article by Fraser Speirs who is a developer at Connected Flow and Head of Computing and IT at Cedars School of Excellence to learn more about iOS multitasking features and how non-active apps are handled.  [Note 2021:  Fraser Speirs’s article is not longer available but a summary can be found on Daring Fireball here.]

Update Feb 2015: Sometimes quitting an app isn’t sufficient to resolve the issue that you’re having. If you find yourself in this situation then you might need to perform a hard reset of your iPhones or iPad.