Graduation hats are called mortar boards because they are similar in appearance to a masonry tool that has a square board, with a handle, for carrying mortar bowls..
Graduation hats are also called square graduation caps or Oxford caps. The hats were adopted from the attire worn by English college graduates since the 14th century at colleges like Oxford University.
Outside of the U.S., graduations hats are sometimes referred to as squares, trenchers or corner-caps.