What does the "principle of deferred decisions" formally mean
The principle of deferred decisions is the concept that we have two ways to make a random choice both of which are equivalent. 

One way is that you can toss a coin yourself at the exact step when you need a random input in some algorithm. In the other way you can imagine that there is an oracle who has already tossed a coin infinitely many times and has some sequence of the form $HTHTHH\dots$, and we query this oracle to tell us the next randomized outcome.

Basically we can defer the act of actually using a randomized input for  as long as we have to and this won't affect the randomness of this input.