A besom, or broomstick, is as much part of the traditional image of a witch as a pointed hat. The difference is, witches do still use besoms. Not for flying about on - obviously - but for sweeping the room before working magic.
I suppose you could use an ordinary broom, or even a Dyson, but an old-fashioned besom makes a symbolic connection to times gone by and all the witches in history who have prepared their magical space. Besoms are also pretty good for clearing up leaves in the garden.
In centuries past a besom was a common household item used for sweeping the house or yard. The broom was made from a tightly-bound bundle of twigs - usually birch - with a wooden shaft inserted into the centre. They certainly weren't only used by witches
The other myth about besoms is that witches use them to apply hallucinogenic drugs to their personal regions for a private thrill.
There is little evidence that witches ever used their brooms for such sensational purposes, or at least no more than any other single woman might have eyed up a curiously-shaped item before the advent of Ann Summers. It just makes a titillating story.
Here are some links to sites on how to make a besom and more about their history and magical use today: