elongated piece of wood or similar material, typically put to some use, for example as a wand or baton
A baton is a stick. Different batons are used by different people, for different things.
Policemen often carry batons, which can be used as weapons. These batons are also sometimes called "nightsticks."
Runners pass batons to one another in relay races.
Musical conductors use batons to lead an orchestra.
Various people in a parade or marching band might twirl batons for people to see.