Otaku literally means "house" or "home" in Japanese, but it is often used in Japan to refer to someone who is devoted to a hobby to the point of obsession. Otaku in Japan indulge in a wide variety of hobbies (i.e. video game otaku, action figure otaku, Internet otaku, etc.), but share the commonality of being near shut-ins who focus on little else. It is considered a derogatory term in Japan.
In Western culture, the word otaku has been borrowed as a word for someone who tends to like anime and manga (one particularly popular Japanese hobby) more than most other people. An otaku in this sense isn't necessarily a shut-in and may have other hobbies and interests. The term is generally used in a sense of commaraderie in this case.