High ankle sprains are different from (lateral) ankle sprains. They happen to a different part of the ankle. Instead of happening to the outside of the ankle, this involves ligaments located right above the ankle joint that connect two bones of the lower leg (tibia and fibula). The way it happens is also different. Instead of twisting the ankle, an athlete usually lands awkwardly forcing the ankle to dorsiflex. He/she may land on someone's foot or an object. In young athletes, (growth plate) fractures or avulsion fractures may also happen, especially the mechanism of injury involves twisting motion.
But why is it more difficult to treat? The reason is that it puts stress on the ligament every time the injured ankle bears body weight. When you take a step, a ground reaction force (GRF) from the ground is transmitted through the ankle forcing tibia and fibula to separate from each other. Anterior tibiofubular ligament (the most commonly injured ligament in high ankle sprains) holds the bones together. However, in an injured ankle, this puts stress on the ligament causing the pain. Depending of the severity of the injury, the athlete may be on crutches until pain resolves, or partial weight-bearing. Also, most ankle braces are designed to prevent lateral ankle sprains and do not prevent high ankle sprains.
Especially, in sports that involve lots of jumping such as basketball, volleyball, gymnastics, etc., it may be more difficult injury than lateral ankle sprains.