An otaku (おたく) is akin to a 'geek' in English, and is most commonly associated with anime and/or manga obsessed people.
Although it is associated with manga/anime fans that are over-the-top and obsessed, it can mean anyone who is obsessed with any other topic as well. In Japan, the word is looked down upon and is considered negative, as many Japanese people who learn that a person is an otaku may look at them as 'unapproachable'. And otakuism can start out very mild (action figures, manga, anime, cosplay, etc.) and in some cases can elevate to very serious obsession (people falling in love with Dakimakura, decorating their apartments with everything anime and manga, spending their paychecks on more useless items, etc.).
Even though there has been much negativity surrounding the otaku lifestyle due to two large incidents (Tsutomu Miyazaki was known as "The Otaku Murderer" in 1989 because of his strange murders, and in 2004, Kaoru Kobayashi murdered a seven-year-old first grade student), in 2007 the otaku market was worth 186.8 billion yen (about 1.65 billion US dollars).
Akihabara is a notable attraction for many otaku as maid cafes, where the waitresses will dress up and act like anime characters, a perfect center for otaku. Akihabara is also known for the stores specializing in anime and manga related items.
Though because of the negativity surrounding the otaku community, the police have made them primary suspects in cases.