A gray man is someone who blends in to his or her surroundings. If you are out hunting it may be to wear camouflage clothes to look like part of the forest. If you are at a bank it may be better to wear a suit and tie.
Gray men are probably most well known from movies, wearing hoodies, a cap and ordinary jeans, all without logos or special markings.
Look at this video to learn more about the theories behind becoming a gray man.