Homer has two main meanings:

1. A home run in baseball. When a batter hits a homer, they've knocked the ball so far that they can run all the way around the bases and score. Fans leap to their feet when their team hits a homer, especially in close games. Baseball announcers might shout “Going, going, gone!” as the ball sails over the outfield fence for a homer. Players who hit lots of homers become famous sluggers.
2. Someone who shows unfair favoritism toward their own team, city, or group. A homer announcer always thinks the home team's players are better, the referees' calls against the home team are wrong, and every victory is deserved while every loss is a fluke. You might notice a homer when listening to a local sports broadcast: the announcer gets excited about the home team's good plays but stays quiet when the visiting team does something impressive. Being called a homer means people think you can't be objective because your loyalty is clouding your judgment.