Beurre manié means "kneaded butter" in French. It's made by working together equal parts flour and soft butter.
It works a bit like a roux, except that the beurre manié is uncooked and added at the end of cooking rather than at the start. Like a roux, it's used to thicken and add flavor to soups, stews and sauces. Unlike a roux, which acts as the foundation for a sauce, beurre manié is often used at the last minute to rescue an overly thin or bland sauce.
Beurre manié can be made ahead and frozen in an ice cube tray so that you'll have it on hand when you need it. Whisk a small knob of beurre manié into simmering liquid and cook for a minute or two to cook out the flour taste. If your sauce or stew needs more thickening, add another knob. (You may need to skim the starch off as it rises.)
Reference: What is a roux? (Cookthink)
Reference: What is a pan sauce? (Cookthink)
Related: Thickening It Old School (A Hunger Artist)