French cuisine is noted for its sauces; rich, varied, and interesting, all of them. When my friend, Lee, asked me to explain them, I came up with this. This is kind of complex, but I think I have distilled it to something understandable and not overwhelming.
The five Mother Sauces are the base sauces upon which hundreds of other sauces are created (those variants are called "small sauces").
Escoffier named them (a huge food guy in the early 20th century who modified a 19th century guy's list of four sauces). Rarely do you see the Mother Sauce used. More commonly served is a variant, a “small sauce.”
Mayonnaise is a small sauce for the Mother Sauce, Hollandaise; Mornay (using Gruyère) is a small sauce for the Mother Sauce, Bechamel; Bordelaise is a small sauce for Espagnole, and so on.
The five Mother Sauces are:
Béchamel (milk base thickened with a white roux)
Espagnole (brown stock base (typically veal) with a brown roux)
Velouté(white stock base with a blond roux)
Tomate (tomato base with roux)
Hollandaise (egg yolks, butter, and an acid like lemon juice or vinegar)
Some have added an oil and vinegar sauce, Vinaigrette
As an FYI, a roux is melted fat, often butter, with incorporated wheat flour, cooked until the flour has no raw taste. Interestingly, the darker the roux, the less thickening power it has!
On a whimsical note, one of the upcoming titles in my culinary mystery series is Roux the Day!