To illuminate is to light up — with physical light or with an idea. A spotlight might illuminate an actor on stage, and a good chemistry teacher might illuminate students with a lesson on the atomic structure of hydrogen.
Originally, the verb illuminate referred to decorating handwritten manuscripts with bright lettering or pictures. Monks illuminated manuscripts with colors like gold, silver, bright red, and blue. Nowadays you can illuminate anything in the dark — either literally or figuratively. If you are afraid of the dark, illuminate your bedroom. In the dark when it comes to organic chemistry? Get an illuminating tutor.