A flexion test is something we do to check for joint injuries. It's normally done with the hocks, and it is done by lifting the leg and holding it with the joint in a bent position, then seeing how the horse moves afterwards.
Flexion tests increase discomfort in the joints if there is an injury or problem, and thus can reveal extremely subtle lameness. There's been more study of them lately - trying to come up with a better protocol (false positives do happen). But they're still a standard part of assessing a horse's condition during pre-purchase exams or competition.