In philately it refers to a postage stamp cut in half, usually diagonally. Bisects were permitted early in the history of postage stamps the late 1840's and early 1850's. Allowed only in the most extreme situations, the last time was over 60 years ago so valid bisect usages tend to be rare and quite expensive. During stamp shortages there were even trisects However, there are only sixteen known "trisect" usages.
Bisects which are not 'tied' (or 'off cover') to the cover by a postmark or cancellation are usually worthless. Anyone can cut a stamp in half, it is the fact that it was accepted as postage that way that makes it valuable. In 1998, a bisect sold at auction for $27,500+15%. Because of the high values in bisects, counterfeits are common.
Today it's illegal to cut, deface or even overlap stamps on US Mail.
The Philippine Philately:Philatelic Words & Terminology: