A baseball bat was a cylindrical object that was used to strike a ball in the game of baseball.
In 2364, Wesley Crusher asked the Edo children he was playing ball with whether they had a bat so he could show them his favorite game. (TNG: "Justice")
Jake Sisko carried a bat and baseball glove on his way to a holosuite when Quark asked what they were for. (DS9: "If Wishes Were Horses")
The Pike City Pioneers chose wooden bats over those made of polyduranide. (DS9: "Family Business")