A "pillbox hat" is a small, round hat that sits on top of the head like a box. It got its name because it looks similar to a container for medication called a pillbox. Full definition
When I found the little pillbox hat with net veil I just knew it would be the right piece to complete the nostalgic feel of this look. (colorandgrace.com)
Just remember Grace Kelly in her all white outfit with pearls and red pumps, or Jackie Kennedy in her baby blue sheath with matching pillbox hat and cropped jacket. (highlatitudestyle.com)
Brides in the 1960s often wore pillbox hats, veils in a bouffant style, and dresses with high empire waists. (businessinsider.com)