Plain English Meaning
It is a small electrical coil at the heart of the flux gate that is fed alternating current to create a changing magnetic field. That changing field is the trigger that lets the rest of the unit detect which way the aircraft is pointing relative to magnetic north.
Full Definition
In a flux gate compass system, the excitation coil is the central winding that receives an alternating current and produces a fluctuating magnetic field within the flux gate's segmented metal frame. This alternating field repeatedly drives the frame in and out of magnetic saturation, which is what allows the surrounding pickup coils to sense the Earth's magnetic field and determine the aircraft's heading.
Context Anchor
Seen in descriptions of the flux gate compass system, especially the that feeds heading information to instruments.