Bioluminescence (literally meaning living light) occurs within many living organisms, although, most are relegated to the deep sea. This chemical reaction involves the oxidation of Luciferin (just a name for a class of biological light emitting pigments). While related, the name doesn't come from any devilish origins, but rather the latin 'lucifer' meaning "light bringer".
Depending on the organism, the light can be used for camouflage, attraction, or even communication among bacteria to name a few. Some of the more notable organisms that bioluminesce include fireflies, glow worms, bacteria, a plethora of marine life, and even mushrooms. (Here's a favorite video of mine from planet earth on the glow worm http://www.youtube.com/watch?v=kBIEmjaoE5w)
Today however, we'll focus on a particular light emitting alga known as Pyrocystis fusiformis. These dinoflagellates typically do not occur in high enough concentrations among marine algae to produce a very noticeable glow. However, when the conditions are right (excess nutrients, enough sun, etc) an algal bloom can occur and populations explode. Chances are you've heard of this phenomenon before which (albeit not involving this particular organism) is also known as a Red Tide.
Here's a video of one such concentration in a bay in australia. They are simply throwing water into the bay as the algae only luminesce when disturbed. A popular theory is that the light is used to attract predators of the grazers of dinoflagellates. Case et al. (1995) demonstrated that the feeding rate of squid of mysids in the dark increases significantly when bioluminescent dinoflagellates are present.
There is even a bay in Puerto Rico full of the stuff which people can kayak in. http://www.biobay.com/
With a little luck and a LOT of patience, you can grow your own bioluminscent algae at home.