Plain English Meaning
Mode C is the setting on your transponder that sends your altitude to ATC automatically, so the controller's screen shows not just who you are but how high you are.
Full Definition
A transponder operating mode that automatically reports the aircraft's pressure altitude to air traffic control, in addition to the four-digit identification code transmitted in Mode A. The altitude data is referenced to 29.92 inches of mercury (the standard altimeter setting) and is transmitted in 100-foot increments when the transponder is interrogated by ATC radar.
Context Anchor
Seen in instrument flying, transponder use, , and rules that require .