Cruises on the Dream will resume on July 2nd, cruises on the Fantasy will resume on July 3rd, and cruises on the Wonder will resume on July 7th. Aside from the Magic at Sea cruises, normal cruises on the Magic are scheduled to resume on September 29th.
This announcement canceled more Alaskan cruises, which are currently impossible because of the Canadian government's cruise ship restrictions. Disney says they are still evaluating options for alternatives to these cruises, but at this point, I doubt they'll need to find an alternative. I think the rest of the Wonder's summer 2021 cruises will get canceled, which would include all of the remaining Alaskan cruises. It would be great for the entire cruise industry if cruises resumed sooner, but with all of the restrictions imposed by organizations like the US CDC, I don't know if they'll be able to.
All of the people affected by this suspension can either get a full refund or, if they've paid the entire price of their cruise, a 125% cruise credit. This suspension will get extended if necessary. The DCL website always is updated with the latest information, so be sure to check there if you're curious.