Nook Miles is a currency that you can earn by performing certain tasks as part of your daily life on your island.
Nook Miles App
The Nook Miles app on your NookPhone shows you the various tasks that you can do to earn Nook Miles. These include things like catching fish, talking to residents, catching bugs, crafting, and so on. Your NookPhone will notify you when you have earned miles or have unlocked a new category of tasks that earn miles. You can claim your miles by going to the completed task in the app and pressing A.
Pay off Tom Nook
You should pay Nook the 5000 miles for your move-in fees as soon as possible, because you won't be able to do much in the game until you do. Be sure to pay him when you have earned enough miles.
You can use the Nook Stop Terminal in the Resident Services Tent to redeem Nook Miles. You can spend your miles on things like new hairstyles, new hair colors, clothing, furniture, and more.
Nook Miles Tickets
You can also get Nook Miles Tickets, which allow you to explore random islands, which helps you find things not available on your island, and introduces you to different animal residents.
When you have paid off Tom Nook, he will upgrade the Nook Miles program to the Nook Miles+ program. This adds more things that you can redeem your miles on, and it adds new tasks to the Nook Miles app that you can do to earn more miles. Just press + when using the Nook Miles app to see the new tasks. These are more short-term tasks, which is helpful for earning miles more quickly. Once you complete one of these short-term tasks, a new one appears.
In addition to earning miles, you will also unlock titles when you claim miles. You can use the Passport App to change the title that appears on your passport. Earning miles gives you more options to choose from for your title.