a stick that is specially designed for some purpose, such as a slender stick used by the conductor of a musical choir or orchestra, or a longer stick with a bulb on one end that is carried by a drum major;
e.g. The conductor lifted his baton and the orchestra prepared to start playing.
(noun)
a hollow rod that is passed between runners on a team in a relay race;
e.g. She passed the baton to the next runner.
(noun)
a short club carried by a police officer, often heavy and made of wood or rubber;
e.g. The police offer carried a baton at his belt.