What does アニメ Anime mean?

Anime (アニメ) is short for animation and means animation of any origin in Japanese. The sense of Japanese animation specifically is an English narrowing.

Written
アニメ (anime)
Literally
A clipping of アニメーション, the loan of English animation. In Japanese it names animation of any kind, from any country.
As slang
Ordinary vocabulary, not slang. Japanese clips long loanwords as a matter of course, and this is one of the least remarkable results.
In anime
English narrowed it to Japanese animation specifically, which is a distinction Japanese does not make with this word and does not need.

Anime is a shortening of the loanword animation. In Japanese it means animation, without qualification: a Japanese television series is anime, and so is a Pixar film, a Czech puppet short and a Saturday morning cartoon from Ohio.

How the word was made

English animation entered Japanese as アニメーション and was clipped, which is the standard fate of long borrowings. Japanese shortens loans constantly, usually to three or four syllables, and the results are ordinary words rather than slang.

There is nothing in the word about Japan, drawing style, target audience or medium. It is the same operation English performs when it shortens influenza, and carries about as much cultural freight.

The English narrowing

English took the word to mean animation made in Japan, which is a category Japanese has no particular use for, since from inside Japan that category is simply animation. Where a distinction is needed the language marks the foreign side instead, in the way any language does.

The English sense is not wrong for English. It names a real body of work with recognisable conventions, and it does so more conveniently than Japanese animation manages in a sentence. It is just not a translation.

The identical thing happened to manga

Both words are ordinary Japanese terms for a medium. Both were borrowed by English speakers who needed a name for the Japanese instance of that medium, and both came back one degree narrower than they left. Manga means comics; anime means animation; English hears Japanese comics and Japanese animation.

The pattern is worth naming because it recurs across this whole vocabulary. A word is borrowed to fill a gap the borrowing language has, and it arrives carrying the specificity of the situation it was borrowed in rather than the breadth it had at home.

The argument the narrowing causes

English-language fandom periodically debates whether a series made outside Japan can be anime. The debate is a product of the borrowing, not a question about Japanese: under the Japanese word the answer is trivially yes, and under the English word the answer is definitionally no.

Both sides are describing their own language correctly. Nothing about Japanese usage settles it, which is why the argument never ends.

One practical note

The stress pattern differs too. English tends to stress the first syllable; Japanese distributes it more evenly with a pitch pattern English does not reproduce. Neither is incorrect in its own language, and this is one of the rare cases where the borrowed pronunciation has not been mistaken for the original.

Quick answers

What does anime mean?

A clipping of アニメーション, the loan of English animation. In Japanese it names animation of any kind, from any country.

Is anime an insult?

Ordinary vocabulary, not slang. Japanese clips long loanwords as a matter of course, and this is one of the least remarkable results.

What does anime mean in anime?

English narrowed it to Japanese animation specifically, which is a distinction Japanese does not make with this word and does not need.