Roux

Roux is flour and any edible fat cooked together and used to thicken sauces. A Roux is typically made from equal parts of flour and fat. The flour is added to the melted fat or oil on the stove top (typically a cast iron pan) blended until smooth, then cooked to the desired level of brownness. (the description under *types) Clarified butter, vegetable oils, bacon drippings or lard are commonly used fats. Roux often is used as a thickening agent for gravy, sauces, soups and stews is, more often than not the base for a dish, other ingredients are added after the roux is complete.
The fat is most often **butter (see types below if clarified butter is not available) is used in French cuisine, but may be lard or vegetable oil; this gave rise to an expression when answering how to make whatever recipe desired as well as the title of a cook book I've used many times "First You Make a Roux".  Roux being the base in three of sauces in classical French cooking: Béchamel sauce, Velouté sauce, and Espagnole sauce. Central European cuisine uses lard in its rendered form (I was brought up on this method our culture being heavily influenced by Europe)
** More recently vegetable oil instead of butter in the preparation of roux vegetable oil is used when producing dark roux, for it does not burn at high temperatures, as butter would (believe you me ya don't wanna burnt roux) In Cajun cuisine, roux is made with bacon fat or oil instead of butter and cooked to a medium or dark brown color, which lends much richness of flavor, albeit less thickening power.
The fat is heated in a pot or pan (melting it if necessary) then the flour is slowly added stirring until there no raw flour taste and the desired color has been achieved. (the final color can range from nearly white to almost black, depending on the length of time it is heated and its intended use. (end result being thickening as well as flavoring)
For meat gravies, fat from whichever meat is often used when rendering. In some regional American cuisines, bacon is sometimes rendered to produce fat to use in the roux.
*Types
Light (béchamel or "white") roux provides little flavor other than a characteristic richness to a dish is used in French cooking and other styles throughout the world. Darker roux is made by browning the flour in oil for a longer time, which adds a nutty and the richer the flavor to the dish .
Dark roux is often made with vegetable oils, which have a higher smoke point than butter, these are used in the making for gumbos and stews. The darker the roux, the less thickening power it has; a chocolate roux has about one fourth the thickening power, of a white roux. A very dark roux, just shy of burning and turning black, has a reddish color and is sometimes referred to as "brick" roux.
                Here are some Youtube videos tutorials  on Roux
How To Make A Roux
https://www.youtube.com/watch?v=aGS89KtrBnM
How To Make A Roux From Scratch - YouTube
https://www.youtube.com/watch?v=y8rWFSbBtak