According to Associate Marine Biologist Ed Roberts, the phenomenon you're referring to is the result of a bloom of microscopic algae known as dinoflagellates.

Some species of dinoflagellates are bioluminescent -- that is, they can create their own light. These bioluminescent cells flash when disturbed.

Thus, when a bloom of bioluminescent dinoflagellates occurs, hundreds of millions of these cells are washed up on the beach, and they light up when you cause a disturbance by stepping on them. When you see this phenomenon, look at the waves breaking on the beach; they will be glowing as well.

This type of bloom is often associated with the phenomenon known as red tide. So the next time you hear that a red tide is occurring, you might want to take an evening stroll on the beach to see if your footprints remain illuminated as you walk along.