Cruciferous vegetables count broccoli, cauliflower and Brussels sprouts among their members. They are classified as being in the cabbage family.
The reason why researchers at the American Cancer Society recommend these vegetables is because they are thought to contain chemicals that can help prevent colorectal cancer, one of the most common cancers today. And being fibrous, they can also help clean up your digestive system.
But remember that all vegetables have beneficial nutrients, so don't just take one kind or family of vegetables; to paraphrase a famous toy line, you gotta try them all!