In modern Japanese slang, the word otaku refers to anyone who is fan of a particular hobby or interest, with varying degrees of obsession. In Japan, otakus can be very specialized in their interest, from cosplay otaku (fans of dressing up in costume) to gemu otaku (video game fans). The English language has adopted the term to refer to a person who is a fan of Japanese animation specifically or a fan of Japanese culture in general.
While the term still carries negative connotations in Japan (often meaning a creepy person, who rarely leaves home and has an unhealthy obsession), it is a term that many in English-speaking countries carry with pride. It’s very similar to the English term geek, which for many years was an insult, but with the advent of modern technology is now a fairly neutral term.