Plain English Meaning
A radio device on the aircraft that talks to ATC radar and other aircraft. It has a unique ID code, so the radar can speak to just your aircraft instead of every aircraft in the sky, and it sends back things like your altitude and call sign.
Full Definition
A Mode S transponder is an aircraft transponder that responds to interrogations from air traffic control radar and other aircraft using Mode Select (Mode S) signals. Each Mode S transponder has a unique 24-bit address assigned to the aircraft, allowing controllers and collision avoidance systems to interrogate one specific aircraft rather than all aircraft in the area. In addition to the basic altitude reporting of older , Mode S can exchange such as , and it serves as the for and .