The tough band of tissue that connects one bone to another at a joint is a ligament.
Ligaments are made mainly of dense connective tissue containing strong collagen fibers. At joints, they connect neighboring bones and help hold the joint together. They can limit excessive movement, guide the direction of motion, and contribute to joint stability. Some ligaments are arranged in layers or crossing bands to resist forces from different angles.
A common mix-up is between ligaments and tendons. Ligaments connect bone to bone, whereas tendons connect muscle to bone. Cartilage is different again: it is a firm, flexible tissue that cushions joint surfaces and can also provide structural support, but it is not the usual name for a bone-connecting band.
Ligaments often have a limited blood supply, so significant sprains may take a long time to heal. A sprain occurs when a ligament is stretched or torn, while a strain generally affects a muscle or tendon. Familiar examples include the anterior cruciate ligament in the knee and the ligaments stabilizing the ankle.