What does お宅 Otaku mean?

Otaku means an obsessive fan. In English that is roughly all it means, and people apply it to themselves cheerfully. In Japanese it is an insult that has softened somewhat and has not stopped being one.

The characters

お (o) is an honorific prefix. 宅 (taku) means house or household. Together they form a formal second-person pronoun, the sort of thing you might use with someone you do not know well, addressing them at one remove by way of their home rather than directly.

That politeness is the joke that became the word. It is a way of speaking to someone while keeping them at arm's length.

How a pronoun became a slur

The usage is traceable to a specific writer. In 1983 the columnist Nakamori Akio published a series in the magazine Manga Burikko observing that a certain type of fan at conventions addressed each other as otaku, and using that verbal tic as a name for the type. His portrait was not affectionate. He was describing people he found awkward and unpleasant, and the label stuck to them.

What fixed it in the general vocabulary was worse. In 1989 the arrest of a serial killer whose apartment contained a large video and manga collection produced a wave of press coverage linking the collection to the crimes. The stigma the word carries in Japan is downstream of that coverage rather than of Nakamori's column, and it is why a Japanese speaker in their fifties hears something quite different in the word than a twenty-year-old does.

What it actually attaches to

Not anime specifically. Japanese uses it for any consuming specialist interest, and the compounds are ordinary: 鉄道オタク for railway obsessives, and equivalents for military hardware, idols, cameras and cars, across hobbies with no fictional content at all. The English narrowing to anime and manga is a borrowing artefact.

Why English took it as a compliment

Because English speakers acquired the word without the 1989 coverage attached, and because it filled a real gap. English has nerd and geek, both of which travelled the same route from insult to self-label, and both of which were already taken by other subcultures. A word specifically for animation fandom, arriving pre-formed and faintly exotic, was useful.

The result is a term that means roughly opposite things depending on who is using it. A Western fan calling themselves otaku is claiming an identity. A Japanese person being called one is being told something about how they are seen.