The Division Championship
If they win that, they go on to the post-season play-off competition to determine who goes on to the World Series.
When the regular season ends after the first Sunday in October (or the last Sunday in September), ten teams enter the postseason playoffs. These ten teams consist of six teams that are division champions by earning the best regular season overall win-loss record for their respective divisions, and four who are "wild-card" teams that are each one of two teams in their respective leagues who have earned the best regular season win-loss record, but are not division champions
This is the 2017 arrangement. In 1989, the year the film was released,
only 4 team made the play-offs (2 divisions from each of the 2 leagues) and there were no wild-card spots.
....the team continues to win and bring themselves into contention for the division championship
The team VP Charlie Donovan visits Brown and informs him of Phelps' plan to make the team lose. He tells Brown that no matter how well they do, they will be fired or released after the season. Brown holds a team meeting and lets the players know of Phelps' plan. Taylor speaks up and encourages the players to win the title anyway, and Brown comes up with a way to motivate them into winning enough games to capture the title.
The team succeeds in tying the division with the New York Yankees, leading to a one-game playoff to determine the champions.