Mother sauces are called mother sauces because they are the foundation sauces to make small, or derrivative sauces. The small sauces are used to make everything from Eggs Benedict, to chicken tetrazini.
The basic Bechemel sauce is the basis for soufle's, gravies, various soups and chowders, stews, etc. Veloute', as mentioned above is the base sauce for soups, stews, and chowders, not to mention gravies as well.
The sauces can be used to enhance the flavors of other foods. Typically, they are spooned over top of something, like with a hot pork, open faced sandwich. The pork gravy is really a veloute' We just don't call it that here in the U.S.
Look up the mother sauces, and you will begin to understand that sauces are the base for so many things we make. And there are many other sauces besides the mother sauces, such as the sauce that is made from brown sugar, mustard, and a bit of tomato sauce to make baked beans. Without the sauce, it's bean soup. There are a host of sauces from other nations as well, such as the sauce that surrounds and adds flavor to chow mien, and all of those wonderful entree's served in Asian restaurants. Sweet & Sour sauce, marinara sauce, sauce creole, mayonaise, Alfredo Sauce, the list goes on endlessly. And I haven't even touched on the mole's (sauces) from Mexico and South America. And then there are curie sauces, and, and, and.
Sauces are the base flavor for so many dishes that it would be impossible to name everything that relies on a sauce. The Mother Sauces are 5 (or six depending on who you talk to) basic sauces that were identified and cataloged by the Famous French Chef, Escoffier. He also gave recipes for the derivative/small sauces made from the Mother Sauces. How you use them is up to you.
Think about this, that wonderful turkey gravy you are so fond of at Thanksgiving is really a type of veloute', though not llisted as such. Typically, Veloute' is made with lamb, chicken, other meats that were common in France when Escoffier was alive. They didn't have turkey or I bet that would have been listed.
There are even sauces made from fish.
Oh, I'm going to stop now. There are just too many sauces to get into on this forum. You could fill several thick books on just sauces. But when you learn the Mother Sauces, you will know enough about sauce making to be able to master most of the other sauces as well.
Seeeeeeeya; Goodweed of the North