C++ variable has initializer but incomplete type?

You use a forward declaration when you need a complete type.

You must have a full definition of the class in order to use it.

The usual way to go about this is:

1) create a file Cat_main.h

2) move

#include <string>

class Cat
{
    public:
        Cat(std::string str);
    // Variables
        std::string name;
    // Functions
        void Meow();
};

to Cat_main.h. Note that inside the header I removed using namespace std; and qualified string with std::string.

3) include this file in both Cat_main.cpp and Cat.cpp:

#include "Cat_main.h"