The phrase "wide brim" refers to a hat or cap with a wide, flattened edge that goes all the way around, providing shade and protection from the sun. Full definition
They were part of Sailor's uniforms in the 1850's (in fact they wore them with wide brimmed hats), and of course experienced a resurgence in popularity in the 1970's. (Whoisapneet.com)
I have been in search for the perfect wide brim straw hat since the beginning of summer, but finding it a bit challenging to stay within a budget. (sugarpeel.com)