What does メカ Mecha mean?

Mecha (メカ) is a clipping of mechanism and covers machinery in general in Japanese. The narrow English sense of piloted giant robots is an English invention.

Written
メカ (meka)
Literally
A clipping of the loanword mechanism or mechanic, written in katakana. In Japanese it covers machinery in general, not one kind of machine.
As slang
Ordinary shortened vocabulary, the sort Japanese produces constantly from English loans. It is neutral and carries no genre implication.
In anime
English uses it to mean piloted giant robots and treats it as a genre. Japanese would more often reach for robot to name that specific thing.

Mecha is a shortening of the English word mechanism, taken into Japanese and clipped the way Japanese clips a great many borrowings. It refers to machinery, broadly, and not to one category of machine.

What the Japanese word covers

Vehicles. Firearms. Computers. Machinery in general.

For the specific thing English means, a large piloted machine with limbs, Japanese is more likely to say robot, which entered the language as its own loan and does the naming work directly.

The English narrowing

English assigned the word to the machines rather than to the category. It then hardened further into a genre label: a mecha series, the mecha shelf, mecha as a thing a viewer either likes or does not.

That genre sense has no equivalent weight in Japanese. A word meaning roughly hardware cannot easily become a genre, because it does not describe what a story is about.

Why the loan was worth making twice

English already had mechanism, obviously, and the loan is a borrowing of a borrowing: an English word that went to Japan, got shortened, and came back meaning something narrower than it left with. Those round trips are common and they usually return with the sense the borrowing community needed.

Here English needed a name for a genre it had no vocabulary for, since giant robot show is accurate and unserviceable in a sentence about tone or craft. The clipped form sounded like a term of art, so it became one.

What the narrowing costs

Mostly it costs a distinction. Japanese can talk about a show's hardware design as a discipline, separately from whether the show is about piloted robots, because the word for the former is not the name of the latter.

English collapses the two, so a conversation about how a series designs its machines keeps sliding into a conversation about genre. The vocabulary makes the more interesting subject harder to reach, which is a small but real cost of borrowing a word one rung narrower than it was.

Quick answers

What does mecha mean?

A clipping of the loanword mechanism or mechanic, written in katakana. In Japanese it covers machinery in general, not one kind of machine.

Is mecha an insult?

Ordinary shortened vocabulary, the sort Japanese produces constantly from English loans. It is neutral and carries no genre implication.

What does mecha mean in anime?

English uses it to mean piloted giant robots and treats it as a genre. Japanese would more often reach for robot to name that specific thing.