Definition
The aircraft heading read directly from the magnetic compass. It is the magnetic heading corrected for deviation, which is the small error caused by magnetic influences from the aircraft itself (electrical wiring, metal structure, instruments). Compass heading is the actual number the pilot must fly on the compass card to track a desired course after accounting for both variation (correcting true to magnetic) and deviation (correcting magnetic to compass).
Plain English
The number you actually fly on the aircraft's compass to stay on the course you planned. It's the magnetic direction adjusted for the small errors the aircraft itself adds to the compass reading.
Context Anchor
Seen in navigation planning, cockpit heading checks, and instructions to steer a specific direction using the magnetic compass.
Derivation
Compass comes from older words meaning to measure or go around, which fits a compass because it divides the full circle around the aircraft into directions. Heading comes from the idea of where the head or front of something points; in an airplane, it means the direction the nose points.
Why Pilots Care
It is the actual indication the pilot must start from before applying deviation corrections to obtain an accurate magnetic heading for navigation.
Intuition Check
Do not confuse compass heading with the path the airplane is actually making over the ground. Compass heading is where the compass says the nose is pointed; wind can make the airplane move along a different path.
Example Sentence 1
After applying the deviation from the compass correction card, the pilot determined a compass heading of 147° to fly the planned route.
Example Sentence 2
Before takeoff the student confirmed the compass heading matched the runway number within a few degrees.