Something that's aflame is on fire. You might accidentally set your marshmallow aflame when you're toasting it over a campfire.
Cherries jubilee is a dessert that's famous for being set aflame at the table, and a stray bolt of lightning can set the roof of a house aflame. In either case, something's burning. You can also use the word figuratively, to describe someone who's very excited: "He was aflame with enthusiasm when he learned there would be a new Harry Potter book." The Latin root of aflame is flamma, "blazing fire."