In probability theory, to postselect is to condition a probability space upon the occurrence of a given event. In symbols, once we postselect for an event E, the probability of some other event F changes from Pr[F] to the conditional probability Pr[F|E].
For a discrete probability space, Pr[F|E] = Pr[F and E]/Pr[E], and thus we require that Pr[E] be strictly positive in order for the postselection to be well-defined.
See also PostBQP, a complexity class defined with postselection. Using postselection it seems quantum Turing machines are much more powerful: Scott Aaronson proved PostBQP is equal to PP.
Some quantum experiments use post-selection after the experiment as a replacement for communication during the experiment, by post-selecting the communicated value into a constant.