I How Does the Equation D x E mod Φ(N) = 1 Relate to RSA Encryption?

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TL;DR Summary
Understanding the RSA mathematics
Please help me understand the RSA encryption.
I understand part of it, then I don't understand.

Definitions:

M=plain text message
C=encrypted message
N=public key
E=encoding key
D=decoding key
P,Q are prime factors on N

I get that
P x Q = N (where P and Q are primes).

I get that

Φ(N) = (P-1) x (Q-1)

I get that

MEmodN = C

I get that

CDmodN = M

But after this I don't understand the relevance of this equation to solve D and E

D x E mod Φ(N) = 1

Seems to be some step or something obvious I'm missing?
 
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