Cabbage worms are caterpillars that grow into moths and butterflies over time. While they are in the caterpillar stage, they eat the leaves of cabbages as well as other vegetable leaves, eventually destroying the plants. If you don't want to use harsh chemicals on your future food, you have few other natural choices that can help keep the worms off or kill them.
Cover cabbage with spun polyurethane once it starts to grow. Use stakes to hold the material down. This keeps the adult moths off of the plants so that they cannot leave their young on the leaves.
Spray the cabbage plants with Bt, which is a biological insecticide. This is needed if you didn't cover the plants with the polyurethane when they first developed. The insecticide has a bacteria that affects the worms. Coat the leaves and leave it for several days, allowing the worms to eat and die.
Cover the plants with the plastic cover a few days after the insecticide application to keep grown moths from re-infecting the plants.
Hand pick off any worms that you see as you are gardening. Every one that you remove is one less you have to deal with later.