A ligament is a connective tissue that connects two bones together. Ligaments provide stability to joints and allow for normal motion of joints in repon=se top muscle forces.
A sprain is a tear of a ligament. (as opposed to a strain which is a tear of a muscle). They are treated based on the severity and location of the ligament injury. Less severe injuries in certain locations usually heal without surgery. Ligament injuries within joints often require surgery to restore normal function.