It's a setting that allows you to use "ADB" (Android Debug Bridge) to perform various operations on the phone over USB from a computer (as long as the computer has the necessary software installed).
As these operations include the ability to copy files (both directions), install or remove apps, and if it's enabled you can do this without unlocking the phone, some people regard it as a security hazard to leave it enabled. Conversely, it can sometimes be used to retrieve data or fix problems when you cannot use the normal android interface to do so (e.g. if the touchscreen is unresponsive).