Cabbage worms are caterpillars. They eat the leaves of a group of plants called brassicas, which includes cabbage, broccoli, kale and cauliflower. They turn into the Cabbage White Butterfly, which is white with some black spots and has a wingspan of about 2 inches. It only takes a few to really damage a head of cabbage. Look for them on the undersides of the leaves.
Watch for any Cabbage White Butterflies in your garden. They are pretty, but they will lay eggs on your cabbage so you don't want them there. Placing floating row covers over the cabbage patch should keep them off the plants. Another trick is to put a nylon stocking over each head of cabbage. Inspect each plant and pick off any cabbage worms or eggs that you see.
Powdering cabbage heads with flour may help. After eating flour, the worms bloat up and die. Getting rid of any old leaves or plants at the end of each season removes eggs that will hatch in the spring. Natural enemies of the cabbage worm, tachnid flies, small wasps and spiders, can be your allies. Attract them with plants they like.
As a last resort, pesticide sprays are available.