This is the traditional four cornered hat of Poland's national folk costume from the Krakow region.  This distinctive hat features a plume of peacock feather.  Why the peacock feather?  See below.

The Kraków regional attire, which began evolving in the 18th century, by the 19th has come to symbolize Polish national dress, even though
each region had its own, often distinctive folk garb. The head-dress of the men's Krakowiak outfit was the konfederatka or rogatywka, the four-cornered cap, which has survived down to the present in the Polish military. Its embellishment was a bunch of rather pricey
peacock feathers which symbolized prosperity, ownership, pride but also (on the negative side) self-interest.
The Polish saying "stroić się w pawie pióra" (to don peacock feathers) means to put on the dog, pretend to be better than one is in actualitiy. Probably the singular attractiveness of peacock feathers are behind the fact that they continue to be reproduced in Polish art forms from pottery to Christmas-tree balls.
Courtesy of Mr Robert Strybel (The Polish Answerman) In Warsaw, Poland.