To luminesce is to shine or glow with light. Some types of jellyfish have the uncanny ability to luminesce underwater.
Glow-in-the-dark paint will luminesce when you turn out the lights, and fireflies luminesce in the night sky during the summertime. There are also many chemicals and minerals that naturally luminesce. A scientist would make the distinction that something luminesces when its light is cool, not hot like a match or a glowing flame. Luminesce, like the related luminescence and luminosity, comes from the Latin lumen, meaning "light."