It controls how far a change to the group's Categories is pushed out when you save:

• Only on new subscriptions — existing subscribers keep their old category restriction.
• Only on renews and new subscriptions — all existing subscriptions in the group get the new category list stored, effective from their next renewal.
• On renews, new subscriptions and open days — additionally rewrites the category restriction on subscribers' open (not yet closed) delivery dates, so it applies to upcoming deliveries immediately.

The dropdown resets to the first option every time you open the page; pick the wider option deliberately.