a ground loop
Suppose two friends both insist they are standing at sea level, but they are actually on slightly different hilltops joined by a long bridge. Anything that rolls across the bridge feels the slope between them. In electronics, ground is meant to be the one agreed zero-volt reference, but when two points both called ground are joined by more than one path, they form a loop, and they are hardly ever at exactly the same voltage. The small difference drives a stray current around the loop, and that current is a ground loop.
Two things create the trouble. First, real ground wires have resistance and inductance, so any current flowing through shared ground copper develops a voltage along it, and your sensitive signal, referenced to that same ground, now rides on top of that voltage. Second, a closed loop of wire acts like a one-turn antenna: any changing magnetic field nearby, especially from the 50/60 Hz mains, induces a current in it. The classic symptom is mains hum, a steady 50 or 60 Hz buzz in audio or 50/60 Hz bars crawling up a video image, that appears only when two grounded boxes are connected together.
The cures all aim at the same thing: do not let ground return current share a path with signal, and do not let the loop enclose magnetic flux. Ground at a single point (star grounding) so currents never mingle; break the loop with an isolation transformer or an opto-isolator; or carry the signal differentially so the loop voltage appears as a common-mode error that the receiver rejects. Honest and important: you usually cannot simply cut the mains safety earth to break a loop, because that earth is there to prevent electric shock and must never be defeated. Break the loop somewhere safe in the signal path instead.
A laptop and a powered speaker are each earthed through their own mains plug, and the audio cable's ground joins them into one big loop. The mains magnetic field induces a current in that loop and you hear a 50/60 Hz hum, which vanishes the moment you break the loop with an audio isolation transformer.
Two grounds, two earth paths, one hum — the signature of a ground loop.
Never solve a ground loop by lifting the mains safety earth — that creates a lethal shock hazard. Break the loop in the signal path (isolation, differential signalling, single-point grounding) instead.