How to Get an iPhone Out of Recovery Mode Without Restoringby Leigh Thompson
Your iPhone may automatically switch to Recovery mode when an error or glitch makes the device inoperable. You can also deliberately enter Recovery mode by pushing a combination of the "Sleep/Wake" button and the "Home" button. An iPhone in Recovery mode has a black screen, and when you plug it into iTunes, it does not register with the software. Instead, an error box appears saying iTunes has detected an iPhone in Recovery mode and you must restore the device. However, if you enter Recovery mode by accident, you can exit the mode without restoring your device.
Plug your iPhone into your computer using your iPhone's USB cord.
Close out the error message in iTunes stating you have to restore your iPhone.
Press and hold the "Home" button and the "Sleep/Wake" button at the same time. The "Home" button is the circular button at the bottom of your screen; the "Sleep/Wake" button is at the top right of your device.
Wait for the Apple logo to appear on the black screen. Your iPhone now boots up and is recognizable in iTunes.