Eventually, you gain access to the Nook Shop in the Resident Services building in Animal Crossing: New Horizons. There are a variety of different options available to you when you open it up, and something you can turn your miles for is a Nook Miles Ticket.
The Nook Miles Ticket is how you go on a Mysterious Island tour, which takes you to a different island than the one you live on in the game. The Mysterious Island is a remote island nearby where you can find a variety of unique specimens and flora than you would find on your island. Before you go on this adventure, you want to clear out as much of your inventory as possible.
When you have your ticket, you want to visit the Dodo airlines at the front of your island, close to the beach. Speak to Orville, the Dodo, who runs the service, and you can redeem the ticket for the ride. The location he’s taking you to is unknown, even to him, so you can’t prepare too much or hold any expectations about what you will encounter. Be prepared for anything, and be ready for some surprises.
There are plenty of things to do in Animal Crossing: New Horizons and the Nook Miles you continually gain will make it easier to explore the game. The more tasks you complete for those Nook Miles, the more Mysterious Tour you can embark on to acquire resources and add new residents to your island.