Some bites cannot be corrected by moving teeth, because the problem is not the teeth. When the upper and lower jaws are the wrong size or in the wrong position relative to each other, braces alone can only camouflage it.
Orthognathic surgery repositions the jaw itself. It is performed by an oral and maxillofacial surgeon in hospital, with orthodontic treatment before it to line the teeth up for the new jaw position, and after it to settle the bite precisely.
It is a significant undertaking and we treat the decision seriously. Many patients who could have surgery choose not to, and there is nothing wrong with that choice, but you should make it knowing exactly what each route can and cannot achieve.