The muscle on the opposite side of a joint from the one doing the work, which lengthens and controls the movement rather than driving it.
In a biceps curl the triceps is the antagonist; in a leg extension it is the hamstrings. The antagonist is not passive. It stays lightly active to keep the joint stable and to slow the limb near the end of the range, which is why a rep thrown fast into lockout is harder on the elbow than a controlled one.
The practical use is antagonist pairing: alternating a set of one muscle with a set of its opposite, such as a chin-up followed by an overhead press. Rest between the two is short (about 60 seconds) because the muscle resting is not the one working, so a session that would take 40 minutes as straight sets takes about 28.
Pair by joint, not by feel. Rows with presses, curls with extensions, leg curls with leg extensions.