This is a baseball phrase which refers to the slow run of a runner around the bases after they have hit a home run. A player may start their home run trot as soon as they hit the ball, or as they are running the bases. It is important that a player not start their home run trot too early, just in case the ball does not go over the outfield wall. This action is considered showboating and gloating. It is not performed after every home run, only those where the player wishes to celebrate the accomplishment.
A typical situation where a home run trot may be performed would be after a player hits a walk-off home run. This is when the team wins the game and ends it with just one hit. If the game is important, such as the playoffs or World Series, the potential for a home run trot increases because the stakes in the game are much higher. Some players take pride in their home run trots and others never do it.