A coil of wire near a magnetic field picks up electromagnetic signals and acts as a low-frequency antenna or microphone
Any coil of wire in a changing magnetic field produces a voltage—this is the principle behind microphones, speakers, and guitar pickups. A telephone pickup (inductive tap coil) is simply such a coil sold for eavesdropping on phone handsets. When connected to an amplifier, it picks up electromagnetic fields from computers, motors, power lines, cell phones, and speakers—translating invisible electromagnetic activity into audible sound. Unlike an air mic, it is directional at millimeter scale (stethoscope precision), allows mapping circuit boards by listening to their electromagnetic emissions, and can be used as a Theremin-like instrument when brought near a speaker (feedback between the coil and the speaker’s voice coil creates pitch dependent on distance). Guitar pickups are simply more expensive coils in this same family.
Examples
Drag a telephone pickup coil across a laptop surface while it boots; each component zone (CPU, RAM, CD drive) sounds different. Hold the coil near the speaker of your amp for Theremin-like distance-controlled pitch.
Assessment
Why does a telephone pickup coil hear things differently from a microphone? Explain why ‘single coil’ guitar pickups pick up more hum than ‘humbuckers.’