What does #include actually do?

In C (or a language based on C), one can happily use this statement:

#include "hello.h";

And voila, every function and variable in hello.h is automagically usable.

But what does it actually do? I looked through compiler docs and tutorials and spent some time searching online, but the only impression I could form about the magical #include command is that it "copy pastes" the contents of hello.h instead of that line. There's gotta be more than that.