Summary

Think of a function as a black box.
A "black box" is a convenient analogy for something that happens by magic. How does the black box work? It takes some inputs, and swirls them around inside the box, and produces some kind of output. Each function can swirl around the inputs in a different way, however that function so chooses. How a function will use the inputs to come up with the outputs is the essence of the function.
We just said that functions are like black boxes because we throw in some inputs, and something happens by magic, and some output comes flying out. The black box metaphor is really only appropriate when you are using other people's functions. When you write the function yourself, you have to know exactly how the function swirls up the inputs. It's not magical for you, because you decided how the function works. However, if you give your function to someone else for them to use, you can tell them it's a black box.