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iPhone DFU(Device Firmware Upgrade) mode is a state you can put your iPhone into where it can interface with iTunes but does not load the iOS. In DFU mode, you will see just white background on the screen while recovery mode shows the "Connect to iTunes" sign.

The most common use for DFU mode is to jailbreak, but sometimes it got your iPhone stuck with the black display and you keep getting error codes. To get out of DFU mode without restoring your iPhone, you can simply take the following steps:

Manually get out of DFU mode

1. Start iTunes and connect iPhone to your computer;
2. Hold down both HOME and Sleep/Wake buttons for 10 seconds;
3. Hit the Power button and wait until your iPhone restart.

Exit DFU mode with RecBoot

If this does work, you can use a tool like RecBoot (Mac OS X only) and follow the instructions below.
1. Install & launch RecBoot;
2. Plug in your iPhone;
3. Click on “Exit Recovery”.