The Multi-Season League settings within the League Rules step of the Theme League Wizard are geared towards progressive leagues (leagues which stay together for more than 1 season by typically advancing players from 1 season to the next).
If you're starting a Progressive League, you'll want to check the "Start a new multi-season league" box. This flags the league as a special league that will allow future leagues to tie back to it.
If you're continuing a Progressive League, you'll want to enter the previous league's League # and the password for the progressive league.
When a league is flagged as a Multi-Season league, league members can view the standings, stats and trade history for all previous leagues within the "chain" of the progressive league. In addition, the Team Profile page of teams in the league will have a special feature to view the previous or future season outlook of a team. That is, you can view who will be available and what the actual stats are for team's players for seasons in the future or in the past. The Draft Center will also have some additional options that allow you to load your previous season's roster and offset the year by a specified amount. So, you can load your previous season's 1910 team with a season offset of 1, and it will load the 1911 version of the roster.
In addition, your Team Notes will automatically carry over to the next season as Draft Center Notes. These Draft Center notes then carry over to your Team Notes. This allows teams to keep track of their injured reserve and other multi-season related information.