Definition
A flight instrument that displays the airplane's heading — the direction the nose is pointing — referenced to a compass rose graduated in degrees from 0 through 360. It is gyroscopically driven (mechanically or electrically) and must be periodically aligned with the magnetic compass, because the gyro itself does not seek north.
Plain English
An instrument on the panel that shows which way the airplane's nose is pointing, in degrees around a circle. The pilot uses it instead of the magnetic compass because it is steady and easy to read in flight.
Context Anchor
Seen during basic flight by reference to instruments, instrument cross-check, and any time an instructor or controller asks you to hold or turn to a specific heading.
Derivation
Heading' here means the direction the nose is pointing, not the direction the airplane is actually travelling over the ground (that is 'track' or 'course'). The instrument is called an 'indicator' because it shows the value rather than measures it from scratch — it is set by the pilot from the magnetic compass and then holds that reference using a gyroscope.
Why Pilots Care
It gives a stable heading reference that is far less affected by turns and acceleration than the magnetic compass.
Intuition Check
Heading does not mean the exact path the airplane is moving over the ground. Heading is where the nose points; wind can make the airplane's actual path over the ground different.
Example Sentence 1
After takeoff, the pilot turned right until the heading indicator showed 090 degrees.
Example Sentence 2
During the cross-country leg the student kept the heading indicator centered on 090 to stay on course.