Beurre manié is softened butter kneaded with flour into a smooth paste. Small pieces are whisked into a hot sauce or soup, then cooked until the flour thickens the liquid and loses its raw taste. Coating the flour with fat helps disperse it.
Unlike roux, the mixture is not cooked before it goes into the liquid. It is also different from beurre monté, which is a butter emulsion without flour.
Reference: Further reading.