A ligament is the tissue that connects two bones to form a joint. It's tough and fibrous, which means that when it tears, a ligament can take quite a while to heal and might even require surgery.
Ligament comes from the Latin ligare meaning "to bind, tie," which is precisely what a ligament does. Ligaments only connect bones to bones. Ligaments allow for range of motion. Think of how your knee or elbow is able to move up and down like a hinge. That's thanks to the ligaments connecting the bones to form knee and elbow joints. Over time, ligaments gradually stretch. If you've ever met someone who is "double-jointed" that means their ligaments are extra elastic, which lets them stretch more than the average person.