I have seen this in articles describing the varios types of namespaces. I fail to understand the code. Could you help break the code down for me?

anyway no fun with broken code =)

Defining functions on prototype is usually a better idea: http://stackoverflow.com/questions/4508313/advantages-of-using-prototype-vs-defining-methods-straight-in-the-constructor

Nope @arichidoru, in fact it's even clearer the way you've put it. []s

Is there any particular reason for adding sayHello() via MyClass.prototype and not directly in the MyClass = function(phrase){this.phrase = phrase; this.sayHello = function(){return this.phrase}}?

The description didn't say not to overwrite a falsey value. It said not to redefine an existing namespace.

I understand your concern about falsy values, but this does not fix this (unlikely) scenario. In case MyNamespace is 0 (or any other primitive value) your code would fail on this line:

MyNamespace.MyClass.prototype.sayHello = function () { return this.string; }

Since MyClass reference will be discarded right after the number is coerced to an object. Another example below:

var n = 0;
n.MyClass = function(){}
n.MyClass.prototype.sayHello = function(){} //TypeError: Cannot read property 'prototype' of undefined