When you overload an operator and use it, what really happens at compilation is this:
Foo a, b, c;
a = b;
//Compiler implicitly converts this call into the following function call:
a.operator=(b);
So you can see that the object b of type FOO is passed by value as argument to the object a's assignment function of the same type. Now consider this, what if you wanted to cascade assignment and do something like this:
a = b = c;
//This is what the compiler does to this statement:
a.operator=(b.operator=(c));
It would be efficient to pass the objects by reference as argument to the function call because we know that NOT doing that we pass by value which makes a copy inside a function of the object which takes time and space.
The statement 'b.operator=(c)' will execute first in this statement and it will return a reference to the object had we overloaded the operator to return a reference to the current object:
Foo &operator=(const Foo& rhs);
Now our statement:
a.operator=(b.operator=(c));
becomes:
a.operator(Foo &this);
Where 'this' is the reference to the object that was returned after the execution of 'b.operator=(c)'. Object's reference is being passed here as the argument and the compiler doesn't have to create a copy of the object that was returned.
Had we not made the function to return Foo object or its reference and had made it return void instead:
void operator=(const Foo& rhs);
The statement would've become something like:
a.operator=(void);
And this would've thrown compilation error.
TL;DR You return the object or the reference to the object to cascade(chain) assignment which is:
a = b = c;
T&
(Foo&
in your example). – Inositol