- Up until the early 1950's when men wore hats it was etiquette when they met a woman or entered a building; especially a church, that they removed their hat. Most men do not wear hats and if they do it may be a Golf hat or a sports hat of some sort and there is no need to remove their hat. In some military schools taking one's hat off is customary on certain occasions.
Removing one's hat has been a sign of respect since medieval times. It began by removing the hat in church to show respect for God.
If you tell someone "I take my hat off to you," then you are saying "I acknowledge your superiority in that subject or event."