Compound butter is simply butter with an added flavor or two mixed in. It's not just like buttering an item and then adding a sprinkle of the flavor - compound butter becomes a unique flavor unto itself. You can put these on pastries, meat, pasta - anything you like.
You want to something special for a party, but the recipe calls for cake flour and buttermilk and all you have is all-purpose and 2%. It's happened to the best of us. Luckily, there are substitutions for these no-so-common ingredients that you can whip up with items you likely already have in the cabinet (baking soda! cornstarch! lemon juice!)