Ground loop
Two devices grounded through different paths, with the signal cable between them completing a current loop — and a stubborn mains hum as the result.
No two ground points in a building sit at exactly the same potential; leakage currents and long runs create small voltage drops. Connect an amplifier on one outlet to a computer on another through an unbalanced cable and a small current flows through the shield, becoming part of the signal. It sounds like mains frequency and its harmonics, often with a whine that changes when the disk spins up or the mouse moves.
Balanced lines tolerate far more. Otherwise the loop is broken on the signal side: the ground-lift switch on a DI box or an isolation transformer. What you never do is defeat the safety earth on the plug. The hum goes away, and so does the protection. A common modern case is a laptop on its charger feeding an audio interface over USB.