A roux is a combination of flour and fat which is commonly used as a thickening agent in cooking of stews and sauces. A roux can also be used as a base for various Classical French sauces, such as Bechamel or Velouté.
To make a roux the fat is melted and an equal part flour is stirred into the fat until incorporated. This mixture is then cooked, releasing the starches from the flour and removing the raw floury taste, until the flour has a toasted aroma. What type of fat is used and how long the roux is cooked for will depend on what it is to be used for and cultural preferences.
A light coloured roux will usually be used as the base for a classical sauce where it's primary use is as a thickening agent ( think macaroni and cheese). A darker, "red" roux, is one that has been cooked longer and has developed more of nutty full flavour.
The Cajun/Creole cuisine traditionally combine vegetable oil not butter with the flour and cook it longer. The vegetable oil has a higher smoke point than butter and results in a darker colour roux with a richer flavour.
If flour were simply added directly to a hot liquid the flour would form clumps or lumps. By " cooking" the flour the starches are allowed to expand and enables it to absorb the moisture added.
Once cooked to the desired colour the roux should be used immediately.
Many of our recipes have a roux as a part of the recipe, even if it is not called a roux.