Plain English Meaning
A fluxgate is a magnetic compass with no moving parts, mounted away from cockpit electrical noise, that senses which way is magnetic north and feeds that heading to your cockpit display electrically.
Full Definition
A fluxgate is a small, fixed magnetic sensor mounted in a stable part of the airframe (typically a wingtip or tail) that detects the direction of the Earth's magnetic field and sends that heading information electrically to the aircraft's heading indicator or HSI. It uses a ring-shaped iron core wrapped with coils; an alternating current drives the core in and out of magnetic saturation, and the surrounding Earth's magnetic field induces a measurable signal in the that varies with the sensor's to magnetic north.