"He hath eaten me out of house and home..."See in text(Act II - Act II, Scene 1)
Sir John Falstaff has been unwilling to take care of his tab at the Boar's-Head Tavern. Hostess Quickly complains to the Chief Justice and she threatens Falstaff saying that she'll visit him like a nightmare. He retorts with a characteristically vulgar interpretation of her threat. This famous phrase has been adopted exactly as Quickly uses it here, which means that Falstaff has not only eaten all of Quickly's provisions, but he has also consumed (or disturbed / drained) her domestic comfort.