If Disney cancels the cruise,
Disney Cruise will refund your money for the cruise automatically. If you have airfare or other expenses (e.g., hotel, car, private excursions) not booked through Disney, though, you would need to file through insurance for reimbursement if you have non-refundable costs or cancellation fees.
I was booked on a Dream cruise that was cancelled in October 2017 because a storm was expected to hit Orlando and Port Canaveral. Disney Cruise offered a discount on a future cruise within the next year, as well as a full refund. Because the storm was hitting Orlando, our flight was cancelled anyhow and we were able to cancel hotel and car reservations with no penalty.
As lanejudy noted, a cancellation is rare, and will typically happen only if the storm is expected to affect the area right near the departure port. If a storm is expected to affect other ports, the ship may simply be sent in a different direction (as the Fantasy was this week). This could result in different ports and/or additional sea days. Disney Cruise will cancel or move any excursions booked through them at ports you don't visit or visit on a different day. Most private excursion companies say you will not be charged if your ship doesn't dock at the port, but if you do have private excursions booked, you'll want to check on the policies.