A cinnamon stick is really a scroll of tree bark. Strips of bark are peeled off cinnamon trees and left to dry, and as they dry they curl up all by themselves into the little rolls you see in the spice aisle.
Cinnamon trees are evergreens with long glossy leaves and small clusters of flowers. Harvesters peel the bark in strips, scrape off the rough outside and keep the thin inner layer, which is the part that ends up in your kitchen.
Cinnamon bun dough gets rolled out flat and spread with butter, cinnamon and sugar. Then it's rolled up like a sleeping bag and sliced into rounds, and every slice keeps its swirl as it puffs up in the oven.
Mexican hot chocolate has cinnamon mixed right in. It's traditionally whipped frothy with a carved wooden whisk called a molinillo, and a cinnamon stick makes a handy stirrer.