A petasos is a style of hat, usually made of felt, with a broad, floppy brim. It was worn by farmers in classical times, and was considered characteristic of rural people. The name is the Greek and Latin word for any hat.
A similar hat was worn by hippies.
Representations of the Classical god Mercury (mythology) are often identified by a petasos, which he often wears. His petasos usually has little wings attached.