Plain English Meaning
Mode A is the part of the transponder reply that tells controllers which aircraft you are. Mode C adds your altitude to that reply. Together they let ATC see your identity and height on their radar screen.
Full Definition
Two transponder reply formats used by Secondary Surveillance Radar. Mode A returns the four-digit identification code (squawk code) assigned by ATC. Mode C returns the same identification code along with the aircraft's pressure altitude, encoded in 100-foot increments referenced to 29.92 inches of mercury. Both modes operate by replying to interrogations transmitted from a ground-based SSR antenna.
Context Anchor
Seen in procedure notes and equipment requirements for instrument departures, including departures, when and are required.