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.

Sources:

Alphabetilately:
http://alphabetilately.com/WMS.html

The Philippine Philately:Philatelic Words & Terminology:
http://www.fortunecity.com/victorian/byron/107/term1.htm

Bisecting a line segment
Open a compass to more than half the length of the line. Place the compass's point on one endpoint of the line, and draw a circle centered at it. Repeat for the other endpoint of the line. Draw a second line connecting the intersections of the circles. Where the second line meets the first is the midway point for both.

Bisecting an angle
At the vertex of the angle, place the point of the compass. Draw an arc with the compass that strikes both the angle's legs. Where the arc meets each leg, place the compass point there and draw a circle (leave the compass at the same radius as before). The circles intersect at two points: one is the vertex of the angle, and if you draw a line connecting it to the other point, you'll have cut the original angle straight in half.

Bi*sect" (?), v. t. [imp. & p. p. Bisected; p. pr. & vb. n. Bisecting.] [L. bis twice + secare, sectum, to cut.]

1.

To cut or divide into two parts.

2. Geom.

To divide into two equal parts.