Well, the main reason would be for separating the interface from the implementation. The header declares "what" a class (or whatever is being implemented) will do, while the cpp file defines "how" it will perform those features.
This reduces dependencies so that code that uses the header doesn't necessarily need to know all the details of the implementation and any other classes/headers needed only for that. This will reduce compilation times and also the amount of recompilation needed when something in the implementation changes.
It's not perfect, and you would usually resort to techniques like the Pimpl Idiom to properly separate interface and implementation, but it's a good start.