Recovery Mode is an alternate boot-up screen that allows you to sometimes fix or mod the phone.
The stock recovery screen will generally allow you to factory reset, clear cache, install a file named update.zip on the internal SD card, though it usually won't allow that due to security measures on the device.
There are custom recovery modes, such as ClockworkMod Recovery which have a lot more features that the stock recovery screen.

How To Access Recovery Mode:
  • Button Combo - While device is powered off, press and hold both volume keys. While holding them, press the power key down for about 4 seconds (until the screen comes on). Release the power key, and continue holding the volume keys until you are in recovery mode.
  • Reboot Application (requires root)
  • CMD/Terminal
    1. Install ADB
    2. You must have USB Drivers installed for your device.
    3. Enable USB Debugging on your device and plug it into your computer via USB cable.
    4. Open CMD (windows) or Terminal (linux/mac). To open CMD, hold windows key, then press R, then type cmd.exe and press enter.
    5. Type adb reboot recovery