A high-waist trouser sits above your natural waist rather than down on the hip, and it is one of the most flattering things you can put on. It lengthens the leg, brings the torso back to a sensible proportion, and it pairs naturally with braces, which are both more comfortable and more correct with this cut than a belt will ever be. It was the tailoring standard for a very long time, until the fashion trade decided everything should sit on the hips.
What the extra rise actually does
The logic is not complicated. The higher the waistband sits, the longer the leg reads and the shorter the torso looks against it. If you are tall, that gives you a handsome length of leg. If you are on the shorter side, it fixes the exact problem a low-rise trouser creates, which is a short leg set against a long body. Most men are surprised by how much difference two inches of rise makes in the mirror.
These are trousers for braces, not belts. Braces hold the trouser up from the shoulder instead of gripping it around the middle, so the cloth hangs rather than being clamped in place. What you get is a straight clean line from waistband to break, with none of the gathering and bunching at the waist that happens when a belt is doing all the work and you have been sitting in traffic for forty minutes.