A roux is a mixture of cooked butter and flour. Cooking the roux to various stages of darkness (from light to dark) imparts additional flavour to your dish. The longer you cook a roux, the darker it gets, and the less its thickening abilities are. Beurre manié is not cooked before use, and although it may not add more flavour to your dish, it is foolproof as a thickener, especially if you are a beginner in the kitchen.