Mush is a soft, squishy clump of something. That bowlful of mush your grandfather gave you for breakfast might be oatmeal.
Mush is a soggy mass, and cornmeal mush is a kind of porridge that fits this description. Mush is also something so overly sentimental that it's almost disgusting: "Oh, that movie was terrible, just a bunch of romantic mush!" When you use mush as a verb or an exclamation, it's usually in the context of dogsledding, meaning "Go!" or "Move forward!" This last meaning comes from the French marche, "walk" or "go."