Self-tapping is the ability of a screw to advance when turned, while creating its own thread. This ability is sometimes created by a gap in the continuity of the thread on the screw. These edges cut a thread as the screw is driven in to the material. The cutting edge drills away the material, leaving a hole for the screw to go into.
Self-tapping screws are used in a variety of applications ranging from DIY to surgery. A dental implant is an example of a self tapping screw used in surgery.