iPhone relieve: Apps in the Background close
The simplest cause would be that too many Apps are running in the Background.
- Press twice on the Home Button.
- To close a window, pull it up and out of the screen.
- Closing the Apps does not help, try a restart. This allows you to clean up the memory of your iPhone.
Storage space, if the Iphone is jerky
Also a restart doesn't help, next step is to check how full the memory of the device.
- Tap in the settings on the "General" and then on "Info".
- Check how much memory is still available. You can find this information under the term "Available".
- Less than 500 MB should be available, it may be the cause for the stuttering. You can delete Apps, music, pictures or other large files to create space.
- Tip: Under "settings - General - use" you can see which files and Apps up the most disk space.

Free memory on the iPhone
iPhone reset
All this does not help, the last resort, the restart of the device. How does it work learn here.
The manual refers to a device with iOS 7. A comparison between the different models you will find here.