Undergo means "endure until something is complete." You might undergo testing to check your hearing or undergo special training if you want to volunteer at a homeless shelter.
The verb undergo means "experience" or "undertake." It is often used to describe medical procedures, such as, an injured quarterback who will undergo shoulder surgery. The word implies that it is something that has to happen so that a positive change occurs, like healing in the case of the quarterback or greater communication skills for a hot-tempered person who undergoes anger management training.