Something is carcinogenic if it has the potential to cause cancer. Cigarettes, for example, are carcinogenic because studies show that smokers are more likely than non-smokers to develop certain kinds of cancer.
To correctly pronounce carcinogenic, accent the fourth syllable: "car-sih-nuh-JEN-ick." Carcinogenic is related to the noun carcinogen, meaning "a cancer-causing substance." Both words come from carcinoma, or "malignant tumor" and -gen, a suffix that means "something produced." So something that is carcinogenic produces malignant tumors — cancer.