"To win the league" means to be the best team in a specific sporting competition. It refers to the team that finishes first and is declared the overall winner of all the teams that participated in that league. Full definition
You can't win the league with more than 5 loses. (justarsenal.com)
The Gunners must hold onto their star players if they are to have any chance of winning the league title this season. (soccerisma.com)
So we haven't won the league in over a decade and the closest we've came was last season where we still lost out to a team that just got promoted that season. (justarsenal.com)