The term "otaku" seems to have been introduced to anime fans in the US and other countries via Studio Gainax's "Otaku no Video 1985," a self-parody film.
Otaku, meaning probably "venerable house," refers to someone who has a devotion to a subject or hobby (not necessarily anime) to the point of not leaving home. For instance, an otaku fan of a particular movie star could quite possibly know all of the films s/he has been in, their birth date, time of birth, shoe size, favorite toothpaste, etc. Generally speaking, calling someone an otaku in Japan is an insult, implying that their social skills have atrophied or never even developed, due to their manic involvement in their chosen fandom.
In America, the term is used to denote a zealous fan, usually of anime and/or manga. Due to its introduction to most people's vocabulary through its tongue-in-cheek use in Gainax's film, "otaku" tends to have a much less dire definition overseas.
When dealing with Japanese people, however, it may be best to keep in mind the modern Japanese image of an otaku -- Someone who only leaves their home to eat or shop, if at all, with an overwhelming and unhealthy obsession about something. It can as easily refer to a stalker or sociopath as it can to a harmless anime buff.
Best to avoid the word altogether if one is not sure of the context in which it will be received.