means A close-fitting, stretchy garment that covers the legs, hips, and usually the feet, worn for warmth, dance, sport, or style.

from Exactly what it sounds like: the adjective 'tight' pressed into service as a noun, because the whole point of the garment is that it fits snugly against the skin. 'Tight' itself goes back to a Germanic root meaning dense or close-packed (a cousin of Old Norse 'þéttr'), and English speakers eventually let the close-fitting legwear simply borrow that name — the plural 'tights' echoing other paired leg-garments like 'trousers' and 'breeches.'