A fedora is a felt hat with a wide brim and indentations on top. Many 1930s and 1940s actors wore fedoras in movies.
Most fedoras are creased along the top, or crown, and pinched on either side, and they're sometimes trimmed around the center with a wide ribbon. Although fedoras might make you think of 1920s gangsters or Indiana Jones, the earliest fedoras were worn by women, and even became a symbol of the early women's rights movement. The word comes from an 1882 play, Fédora, in which the actress Sarah Bernhardt wore a fedora.