Vermi-ponics builds on to the concept of aquaponics by incorporating worms into the scenario - yes that's w-o-r-m-s . Unlike fish, worms are pretty much self sufficient - so long as they have a food source.
In a vermiponics system plants and worms flourish together in a soil - less gravel bed. The bed is periodically flooded and drained and the end result is a micro fertilizer factory. Vermiponics basically creates a mini self-sustaining ecosystem, using worm castings as fertilizer. Plants and worms in nature have a mutually beneficial relationship, ditto for the fish in an aquaponic system. Vermiponics however, unlike aquaponics requires less maintenance and less water.
Worms will survive a periodic flooding as in a flood and drain system and their waste product - castings become food for the plants.
So what do the worms eat ? Lacking soil to burrow through they must be fed. In nature worms typically burrow their way through the soil leaving behind a trail of rich fertile castings, in vermiponics they have no soil to burrow through, so hence the worms must be fed.
Finely chopped plant matter such as vegetable scraps, rabbit food, coffee grinds and so forth. Avoid animal waste or meats, although the worms would probably eat it, the potential for bacterial contamination is greater.