Why RSA Works: Three Fundamental Questions Answered

If you're not that familiar with RSA you might want to start with http://doctrina.org/How-RSA-Works-With-Examples.html

But if you've been working through Matasano's challenges and were confused why encryption and decryption seem to be commutative, or why the totient - (p-1)*(q-1) - is used, then equation (1) of the main link could well be the revelation you have been searching for.