In Japanese, Otaku (オタク) means someone who is obsessive about a hobby. Typical hobbies this would apply to would be trains, buses, anime and manga, computers, aircraft, cars etc...
Otaku has a definite negative connotation in Japanese. It is more or less an insult.
Otaku have been portrayed negatively in the Japanese press after a series of crimes have been committed by persons regarded as Otaku. Inside Japan, Otaku are generally perceived to have few social skills.
Outside Japan, anime and manga fans have adopted the word with a more positive connotation meaning a die-hard Anime and Manga fan.