What does ‘otaku’ mean?

What does 'Otaku' actually mean?

Is it just used to describe someone who's really into something or fanatical about something?

And is it a negative word, or something 'cute' and maybe 'eccentric' but harmful (maybe like a 'nerd' with not a hostile meaning)?

http://en.wikipedia.org/wiki/Otaku

In japan, otaku has two meanings. Obsessive nerd with a particular hobby and お宅 "your honorable home" which the slang term is derived from since they seemingly spend their entire time in their homes. Otakus are viewed as kimoi or disgusting. Nothing is cute about them. The stereotype goes as a man wearing glasses and high pants with a backpack. Maybe sometimes with a pot belly. Due to recent news of killings done in akihabara and the 1989 otaku murderer the otaku reputation has significantly gone done. These perpetrators had their houses searched and collections of anime figurines and other related memoribilia were discovered.
Furthermore, if you ever ask an otaku-seeming person in japan if they consider themselves to be otaku, they will most certainly say, "no". It's ok to watch and play some games, but it's not ok to spend your entire free time doing it or talking about it. It actually might put others off if it's your main topic of conversation.
However, in recent days it seems that if anyone has a particular hobby they spend a lot of time doing, even sports or studying, they may be teased by their friends to be a baseball otaku or an English otaku. Then maybe that person will jokingly agree. It's still not under a positive light unlike places like America where some proudly call themselves otaku.
This is from my personal experience and also a report competed by a japanese student in a culture class we shared while I was studying in Tokyo. His topic was on otaku. Many of my friends in japan have told me the same.

And is it a negative word, or something 'cute' and maybe 'eccentric' but harmful (maybe like a 'nerd' with not a hostile meaning)?

If you use the word reffering poeple with obsessive interests, especially anime, manga, and girl pop stars called idle, it usually has a negative meaning so that I strongly recommend that you should not call someone otaku. Even though some might not care they are called otaku, but some are hurt and some get upset.

On the other hand it is ok that you call yourself otaku if you don't care.
If you love mathematics, you can call yourself math otaku. If you cant help buying clothes, you can call yourself clothes otaku. You can be any otaku.
Sometimes people call themselves something otaku as a humor.

Anyway, be careful about using the word otaku!