Vasectomy is a surgical procedure which permanently cuts off the flow of sperm to the penis. It is the sterilsiation operation chosen by men who no longer wish to father children. An extensive fact sheet about vasectomy can be found here
A 3D description (46 seconds) of the anatomy and physiology and the vasectomy procedure can be seen in the following two videos
Below are some videos explaining the procedures, and showing the difference between types of vasectomy (ligatures and cautery v no closure)
A vasectomy operation using cutting and stitching can be seen below