I suspect the difficulty you are having arises from the fact that post-selection gets mentioned in two similar but different ways.
Experimentally, post-selection refers to discarding experimental runs where something you you wanted to happen didn't happen. For example I have a linear optical network that applies a heralded (get some measurement result to say "it worked!" in addition to the measurement outcome) 2-qubit gate. I want to test my two-qubit gate, so I only look at the runs where I got the result "it worked!"
In quantum computing theory post-selection refers to giving a quantum computer the power to choose the outcomes of certain measurements, which greatly increases its computational power. In this case the, perhaps exponentially many, extra runs required to obtain the output are ignored.
I hope that helps.
This post imported from StackExchange Physics at 2014-03-22 17:11 (UCT), posted by SE-user Q-Anon