In general 'to bisect' something means to cut it into two equal parts. The 'bisector' is the thing doing the cutting.
With a line bisector, we are cutting a line segment into two equal lengths with another line - the bisector. In the figure above, the line PQ is being cut into two equal lengths (PF and FQ) by the bisector line AB.
If AB crosses at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types.
For obvious reasons, the point F is called the midpoint of the line PQ
See also Angle bisector.
Obviously, one way to bisect a line segment is to measure its length, divide that by two and mark the midpoint.
But you can do it without any measurement at all using just a compass and straightedge using techniques developed thousands of years ago by the Greeks. For an animated demonstration of how to do this see Perpendicular bisector of a line segment