Billywigs are flying creatures with a helicopter like set of wings for flying. They also have stingers that inflict a painful sting and cause those stung to levitate for a while and feel light headed. They are rated XX by the ministry as slightly aggressive but nothing a student can't handle. Some people like to let themselves be stung to levitate, but this can cause permanent levitation.
Billywig stings are used in potion making, eg the stamina potion.
Seamus once got stung by a billywig when hanging around the Hogwart's stone henge structure at break time.