Ankle sprains are a familiar term to most people and involve damage to one of the many ligaments around the ankle. An inversion sprain (when you go over on the outside of the ankle) can cause damage to one of a number of ligaments in this area. This sometimes results in a fracture or damage to one of the tendons on the outside of the ankle. In addition, this can cause compression of the bones on the inside of the ankle.
An eversion sprain occurs in the opposite direction and is much rarer due to the bony structure of the ankle joint and the thicker / stronger ligament complex (Deltoid ligament) on the inside of the foot.