The Flying Cap, Aviator Hat, or Bomber Hat is simple a leather hat, fur or felt lined with ear flaps and chin strap to keep it on in the wind, designed to protect and keep your head and ears warm when flying planes with open cockpits back in early days of flight.
These hats are very similar to trapper or hunting hat, the main difference being the ear flaps are longer and don't have ties to fasten them up.
Usually worn with goggles to protect your eyes, I have read most Boeing 747 and Airbus A320 pilots don't wear them anymore which is a shame.
James Bigglesworth is a fictional pilot from around the time of the first world war in books by W.E Johns, he did fly in stories in later wars and between wars, but his book covers regularly showed him wearing a flying cap, for that reasons you may also find this cap or hat called a Biggles Hat
Below is the story in pictures of Richard Bigglesworths James older more hansom brother
Chapter 1 : Biggles Dons His Flying Cap
Chapter 2 : Biggles Wags A Finger
Chapter 3 : Biggle Leans Backwards
Chapter 4 : Biggles Ready To Learn To Fly
Chapter 5 : Biggles Shows The Back Of His Cap