In many cases — such as when talking about money or sentences — compound is the opposite of simple.
But butter is different. Compound butter is simple to make.
Compound butter is just butter with other things in it, and the other things make the butter better.
If you have been to a steakhouse, and they top off your steak with a pat of butter, that’s just butter. But if they top it off with butter that has bits of green in it, or brown, or if the butter is kind of red, that’s compound butter.
Compound butters work so well because fats are terrific conductors of flavor. If you mix a relatively small amount of an herb into a relatively large amount of butter, very soon all the butter will have the flavor of the herb. This is the same reason (or one of the same reasons) that you cook onions or garlic in butter or oil before adding other ingredients.