means A difficult, messy situation that's hard to escape — or, literally, a patch of soft, boggy ground that swallows your boots.

from A 16th-century mash-up of two old words for the same nasty terrain: 'quag' (a marsh or bog, related to the dialect word 'quag' meaning to shake or quake, since the ground trembled underfoot) and 'mire' (an old Norse-derived word for swampy mud, a cousin of 'moss'). So it's literally a 'shaking swamp' — and the doubling-up makes sense, because no single word felt sticky enough.