Definition from Wiktionary, the free dictionary
broomstick (plural broomsticks)
- the handle of a broom (sweeping tool).
- (witchcraft) A broom imbued with magic, enabling one to fly astride the handle.
the handle of a broom
- 1997, Diana Wynne Jones, Witch Week 
- She really was a witch now. No one but a witch could fly a broomstick.
- 1999 J. K. Rowling, Harry Potter and the Prisoner of Azkaban ISBN 0439136369
- Harry ripped the parcel open and gasped as a magnificent, gleaming broomstick rolled out onto his bedspread. [...] It was a Firebolt, identical to the dream broom Harry had gone to see every day in Diagon Alley.
- 2002, Terry Pratchett, Witches Abroad 
- Greebo, hiccuping occasionally, oozed into his accustomed place among the bristles of Nanny’s broomstick. As they rose above the forest a thin plume of smoke also rose from the castle.
- 2003, David Pickering, Cassell's Dictionary of Superstitions 
- Most people are familiar with the age-old superstition that witches fly on broomsticks to their covens (though they were formerly also reputed to use shovels, cleft sticks, eggshells, ANIMALS and other means of flight).