All bones in our body that form joints (some, like those in our skull, fuse together while we are still infants) are held together by ligaments. These are fibrous connective tissues that control how much a joint can move. Try to bend your elbow backwards. It won't go, the ligament will not let it. Ligaments also stabilize the joint, making the bones move in an adequate way (can you bend your elbow sideways?)
Ligaments are formed from crisscross strands of collagen fibers, much as modern carbon fiber hi-tech stuff. Principal difference is that collagen is elastic and slightly stretchy. But not too stretchy. As they support the joint, the ligaments only have a slight margin for "breathing". Stretching exercises, so important for sportsmen and martial artists, actually stretch muscles by increasing their length and flexibility, not ligaments. Actually, a stretched ligament, whether by injury, too much strain or inadequate stretching exercises, makes the joint weaker as it cannot support it adequately (much like a screw that got loose).
Unfortunately, ligaments are highly susceptible to injury. To make matters worse, low blood supply to the ligaments combined with virtually constant stress they must endure make their healing very slow (healing period frequently lasts well over six weeks) and surgery is frequently necessary (just remember how many sport pros had to go under the knife in their career, and how often). The point is that ligaments can heal in an inadequate position and allow for excess movement of the bones in the joint. Physical therapy is frequently required to deal with more severe injuries.
Prevention is better
Once injured, the ligament is never what it was before. It is weaker, less flexible and susceptible to repeated injury. So, you should always watch after your ligaments. Avoid excess straining and stretch properly for starters. There are no specific supplements or FDA approved agents for healthy ligaments, but we can say that a proper diet with adequate levels of nutrients and vitamins helps all of your body, when healing or when staying as it should be, so the same applies to ligaments.
Torn ligament almost always requires surgery.
A strain ligament is usually treated by minimal stress therapy, which means that affected joint will bear no weight or just partial weight while the ligament heals, by means of support or protection such as cast.
If you keep re-injuring your ankle, check if you are using inadequate footwear.
Remember, bones and ligaments heal slowly, and you should not be impatient. Wait until the tissue has regained sufficient strength to function properly without renewing the injury.