The handle of a broom (sweeping tool); (sometimes) the entire broom.
2
A broom imbued with magic, enabling one to fly astride the handle.
Witches of all ages attended these lively gatherings by flying away on their broomsticks[.]1936, Rollo Ahmed, The Black Art, London: Long, page 106:
She really was a witch now. No one but a witch could fly a broomstick.1997, Diana Wynne Jones, Witch Week:
3 more examples
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.1999, J. K. Rowling, Harry Potter and the Prisoner of Azkaban, →ISBN:
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.2002, Terry Pratchett, Witches Abroad, page 97:
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).2003, David Pickering, Cassell's Dictionary of Superstitions:
BATTY: But, Mother Witch, I want to go broomsticking, too.1955, Grade Teacher, volume 73, page 14:
Cynthia the Witch, whenever she broomsticked back into town would not even be given the chance to lay eyes on my machine or my clothes.2006, Brandi Scollins-Mantha, Floaters, page 75: