The Settings app cannot be removed from the phone. It is a native iOS app that is necessary for the operation of the device and cannot be deleted. You may have moved it into a folder. To check, swipe the screen to the right and type in Settings in the search bar. From there, it should appear, and if a folder, the name of the folder will appear as well.
If it appears that your icons have moved down on the screen, that is Reachability. You can just tap on the home button again and they should return to their regular position.