Can someone explain leagues and league points?

Basically you earn league points (blue rosette with magnifying glass symbol) for your team by completing Help Wanted Tasks and playing in Lounge Competitions. Your club competes with other clubs and will win weekly rewards, as well as a League Reward at the end of the 5th week.

At the start of the event, your team is grouped with 9 other teams. At the end of the week, the top 3 teams with the most league points advances to the next division, and they get a greater weekly reward than the others. The teams that don't advance are regrouped with others that didn't advance and start again with league points. The teams that advance to the next division, compete with others that advanced and again start over with league points, vying for top 3 spots to advance again. Divisions are 1-Sleuth, 2-Private Eye, 3-Ace, and 4-Sherlock. At the end of the 5th week, you will get a League Reward based on the highest division your team reached. If your team reaches Sherlock Division, your league points will include all the points that have been banked since the start of the event.

You can also see how your team's total league points compare with other teams globally by tapping on the podium icon in the bottom left corner.