Definition - to stop talking immediately
There is no dearth of occasions on which one might wish to ask others to be quiet, and so it is useful to have a variety of ways in which to make such a request. Zip it is one of the informal ones, a relatively recent (late 20th century) Americanism.
”Oh, zip it up, Carlotta,” said the male voice and went on telling someone about “the divine Fabergé that is on auction right now in Palm Beach. There is no Fabergé in Russia that can touch it; but you knew that, Diane.”
— Edith S. Campbell, Town and Country (New York, NY), Feb. 1976)