Mildew is a kind of fungus that grows in damp environments. If you find a white, musty-smelling powder on a book that's been stored in the basement, it's probably mildew. Yuck!
Mildew and mold are closely related — mildew is a less harmful kind of fungus, though both can cause breathing problems. While mildew is almost always white, mold is darker and fuzzier. Since dampness causes mildew to spread, keeping things dry (possibly with the help of a dehumidifier or air conditioner) can help prevent it. The stickiness of plant mildew helps explain the word's etymology. It comes from a root meaning "honeydew."