Ankles are really prone to sprains, particularly inversion sprains. A sprain is when the ligaments that attach your bones together are stretched and or torn.
The thing about ligaments is that unlike muscle and bones, ligaments do not have a very good blood supply, and therefore do not have the same healing properties that bones and muscles do. In other words, once a ligament is stretched, for the most part, it stays that way. This is why a torn ACL requires surgery to fix, and a broken bone does not.
Now, back to the ankle. After an ankle is sprained, those now lose ligaments will continue to cause instability of the ankle, leading you to constantly re-injure it. The ONLY way to get the stability of the ankle back, and prevent further damage and pain is to strengthen to muscles of the lower leg so that they will help keep everything tight and in it's right place.
Taping and bracing are also used to keep make it so that ankle joint is more stable, but without proper rehabilitation of the joint, it will truly never get better!