A Broomstick Servicing Kit is a collection of items to help keep a racing broom in good condition.
Harry’s mind was on the kit when he he got the unwelcome news that Aunt Marge was going to be paying the Dursleys a visit. He tried using the contents of the kit’s handbook to take his mind off the nasty things Marge was saying about him and his parents. This was unsuccessful (PA2).
From the Web
WizardingWorld.com (Pottermore) features:
Harry Potter Wiki: Brooms