Alternatively referred to as an antistatic strap or antistatic wrist strap, a wrist strap is a strap that wraps around your wrist like a bracelet with a cord that attaches to the computer. The wrist strap keeps the user grounded, which helps prevent electrostatic damage to a computer or any other electrostatic sensitive device. The picture shows a wrist strap with detachable strap around a wrist.
There are also some anti-static wristbands that work by using a battery in the wristband to create a ground. It does not connect to the computer or antistatic mat in this case since the battery power provides the same grounding as a wired wrist strap.
How to use a wrist strap
Place your wrist in the strap and attach the other end (often using the alligator clip) to a non-painted metal portion of the computer case, antistatic mat, or antistatic workbench. While working on the computer or other electrostatic sensitive device the wrist strap should remain on your wrist.