A danish is a sweet breakfast roll filled with custard, jam, or marzipan. If you're invited to brunch at a friend's house, she'll be happy to see you arrive with a box of danishes.
If you order coffee and a danish at a diner, you'll get a flaky, buttery pastry topped with cheese or fruit — not a person from Denmark. The word is short for "danish pastry," which is actually called wienerbrød, or "Viennese bread" in Denmark. The popular history of the danish involves a strike by Danish bakery workers which led bakeries to hire Austrian bakers, who brought their own recipes for pastries rich with butter and egg.