Anime (pronounced AH-nee-may)
Sometimes confused with anime, manga is the Japanese word for comic book (or Graphic Novel, if you prefer) and is used in English to mean Japanese comic books. Manga and anime are very closely related, as artists frequently crossover, as do the characters they create. Usually the manga is created first, and if it becomes really popular then the market it deemed capable of supporting a much more costly animation based on it.
Manga
A term used to describe a style of Japanese animation (cartoon or otherwise) where people are drawn with big doe-eyes. There's also usually at least one of the following large human-controlled anthropomorphic robots; big space ships; ninja, samurai, or other martial arts; demonic entities that spurt tentacles and do really lascivious things with them; people with psychic abilities; cyborgs; or mysticism. The animation is highly stylized, and visuals are often very sharp and glossy. If you're familiar with Akira, Sailor Moon, Star Blazers, or Macross, then you know what we're talking about.
Hentai
In Japanese, the word hentai means metamorphosis, abnormality, or sexual perversion. It is never used to refer to "normal" sexual activity, or to adult manga or other entertainment that is merely sexually explicit.