A roux is a thickening agent made from equal parts butter and flour. The mixture is cooked until the flour taste disappears (about one minute per tablespoon of flour) and then combined with milk or stock to create a sauce. 

There are basically two kinds of roux.

White (or blond) roux is cooked just until the flour taste vanishes, but before the butter begins to turn the roux brown. This becomes béchamel sauce when blended with milk. Combined with stock, it becomes velouté. 

Brown roux is cooked until it turns a nutty brown color. It is used as a thickener for French demi-glacesauce. It can be made with butter, as well as pork or beef drippings. Many Creole and Cajun dishes, including gumbo, use lard to create a dark brown roux. (In our Chicken And Sausage Gumbo, we use less indulgent canola oil. Don't try this in Vermilion Parish; they may jail you for using oil.)

Reference: What is bechamel sauce? (Cookthink)
Reference: Macaroni And Cheese (Cookthink)
Related: Real Cajun Recipes