C++ :: Why Assignment Operator Return By Reference

I have code here that uses assignment operators that doesn't return by reference and it still works. So why does my book say you need to return by reference?

Here is a quote from my book:

The return type of operator= is a reference to the invoking object, so as to allow chained
assignments a=b=c.

The code below is from my book. I simply removed '&', in the original code that has assignment operators return by reference, from IntCell & operator=. This way the assignment operator no longer returns a reference, and it still works.

#include <iostream>
using namespace std;
class IntCell {
public:
explicit IntCell( int initialValue = 0 )
{ storedValue = new int{ initialValue }; }

[Code] .....