In the Earth sport of baseball, the umpire was the person charged with officiating the game. This included beginning and ending the game, enforcing the rules of the game and the grounds, and making judgment calls on plays. The term was often shortened to the colloquial form "ump". They were also addressed as "blue" due to the color of the uniform some umpires wore.
Umpires were also responsible for meting out discipline to the players as a response to a rule violation. For example, making contact with the umpire was grounds for removal from the game, referred to as an ejection.
In 2375, Odo served as umpire for a baseball game between the Niners and the Logicians played in the holosuite on Deep Space 9. He was forced to eject Benjamin Sisko and Solok from the game for touching him. (DS9: "Take Me Out to the Holosuite")