DOMS stands for Delayed Onset Muscle Soreness. It peaks 24-72 hours after training and is caused primarily by eccentric muscle damage, the lengthening phase of a movement. Lowering a barbell during a squat, the downward phase of a bicep curl, running downhill.
DOMS is an inflammatory response. Your body sends fluid and immune cells to the damaged tissue, causing swelling, stiffness, and pain. It is a repair process, not a growth signal.
That is the short version. For the complete guide to DOMS itself (what causes it, the 24-72 hour timeline, how to reduce it, and whether to train through it), see DOMS explained.