Fedoras are soft wide-brimmed hats with a crease in the crown. The word comes from the title of the 1882 play Fédora written by dramatist Victorien Sardou for the actress Sarah Bernhardt in the role of Princess Fédora Romanoff. It later became an opera. (http://en.wikipedia.org/wiki/Fedora_%28opera%29). The hat worn by Sarah Bernhardt became popular among the women's suffrage movement. Later in the 20th century a similar hat was popularized again by Humphrey Bogart.
In 1975 the book Dress For Success, soon followed by Women's Dress For Success, claimed that scientific testing proved that women in a specified "power dressing" uniform (skirted business suits, blouses, silk bows, heeled pumps) were treated better in the workplace. Women's Dress For Success specifically recommended that women wear fedoras. Although the rest of the uniform was widely adopted, the fedora didn't catch on.
In 1982 the television show Remington Steele was based on the premise that the protagonist, professional detective Laura Holt, had to invent a male superior in order for her agency to be taken seriously. In the first season Laura Holt usually wore suits, adding a fedora when outdoors.
In the second decade of the 21st century they became popular as men's wear. Then some feminists began mocking them as a signifier of a particular kind of dudebro in tech/open source. Tumblrs were made, lulz were had. (Link to tumblrs and funny explanations) Then someone else pointed out we could reclaim these cute hats as points of feminist history and pride. There are fedoras, then there are trilbys. There are ironic and unironic, unconscious and reclaimed fedora wearers. Enjoy this bit of history!!!