The main function of USB Debug mode is to establish a connection between an Android device and a Computer with SDK (software development kit). Android SDK is a software suite that is designed for the development of Android apps.

USB Debug Mode also helps in establishing a direct connection between an Android device and the Computer and for deeper-level actions.
USB Debug Mode also helps in providing the required level of access required for system-level clearance.

USB Debug mode is also important when you want to root your Android device.
HOW TO ENABLE USB DEBUGGING ON ANDROIDGoto your device settings, Click About Device
Look for Build number and keep tapping on it repeatedly until it says "You are now a developer"
Goto Developer menu through Settings > Developer options
Under "Developer option", look for USB debugging option then enable it.
That's All!