A roux is a mixture of butter (or another fat) and flour, cooked together to form a thickening agent for sauces or soups. There are three types of traditional roux, used for different purposes:

White roux is usually made from clarified butter and unbleached white flour, so it has a pale yellow colour. It is used for Béchamel and other milk-based sauces and for thick soups. It is cooked only until it no longer has a raw taste and has a frothy and slightly gritty consistency, but hasn’t begun to darken in colour.

Blond roux, sometimes called “pale roux”, is made from equal portions of butter (not clarified butter) and unbleached white flour and used for veloutés, sauces based on white stocks. It is cooked slightly longer than white roux to give it a deeper colour.

Brown roux is made from equal portions of flour and clarified butter and cooked until it turns a light brown colour and develops a nutty flavour. It’s used for darker sauces, such as Espagnole and Demi-glace. Sometimes the flour is browned in an oven before beginning the roux.

The easiest method I have found for using roux in sauces or soups is this: Allow the roux to cool somewhat before adding a liquid to it because it won’t lump as easily. Liquids should be added slowly and mixed with a wire whisk. Once the roux is blended with stock, water, or milk to a smooth consistency, heat it and stir continuously as it thickens. Once thickened, reduce the heat or it may burn.

Note: The longer a roux is cooked, the less effective it is as a thickener. Brown roux is about 1/3 the strength of white roux. Personally, I'd rather deglaze the pan.