Most ankle sprains stretch or tear the ligaments along the outer (lateral) border of the ankle. Sometimes a medial (inside) ankle sprain occurs.
A "high" ankle sprain is used to describe an injury of the ligament that joins the two lower leg bones together. This ligament is called the syndesmosis ligament. The ligament is above the ankle, which is why it's called a high sprain.
This type of injury occurs most often in hockey players and skiers. The foot and ankle get turned out or externally rotated. Since the foot is in a rigid skate or ski boot there's no "give" and the ligament tears.