Q:

What is postselection?

I was reading some questions here. 
I couldn't understand what it means by postselection.
What is postselection? What is its use/significance? Where did it came from?  

A:

One example of where the term "postselection" is used is in delayed choice quantum eraser experiments, such as this one performed by Kim et al.  Here, an attempt is made to determine "which path" information in a double slit experiment by observing the paths of "idler photons" which are produced in combination with the interfering photons of interest.
The important point is that an interference pattern is not produced immediately.  In order to derive the interference pattern from the "mush" of data, you have to look for and select only events in which certain combinations of detectors were triggered.  Since this is "after the event", it's referred to as "postselection".

A:

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.

