If you find an antiquity, call a museum: you just found something very old. Antiquity can also mean the idea of oldness.
The word antique should be a clue to the meaning of this word, which refers to things that are extremely old or ancient. This isn't grandparent old — this is really old, like hundreds or even thousands of years old. People also use this word to compare old ways of doing things to new ways: you could say an old-fashioned idea is an antiquity that goes against modernity (newer ideas and ways of doing things). Antiquity can also mean the time before the Middle Ages.