The term 'boater or bowler' refers to a type of HAT. Boater hats are typically made of straw and have a flat top and brim, while bowlers are made of felt and have a rounded crown. Both styles of hats were popular in the late 19th and early 20th centuries, and were often worn by men for formal occasions. The crossword solution for this term is 'HAT, ' which is an appropriate answer for both types of headwear.