What does お兄ちゃん Oniichan mean?

Oniichan (お兄ちゃん) is a soft word for older brother, and Japanese also uses kinship terms for strangers, which English almost never does.

Written
お兄ちゃん (oniichan)
Literally
Older brother, with the honorific お and the diminutive ちゃん attached. The softest of several forms, the others being oniisan and oniisama.
As slang
Ordinary and affectionate. It is also used for young men who are not related to the speaker at all, which is the part English does not do.
In anime
Heard from younger sisters and, in fandom, associated with a narrow character type. Its everyday use is far broader and duller.

Oniichan means older brother. The interesting part is not the word, it is that Japanese will use it, and terms like it, for people the speaker has never met.

The ladder

The stem is 兄 (nii), older brother, with the honorific お in front and a suffix on the end that sets the tone. With chan it is soft and childlike. With san it is neutral and ordinary. With sama it is formal to the point of being a joke in most households.

A speaker picks the ending according to age, closeness and mood, and can move between them within a conversation. The choice is the same dial that operates everywhere else in the language.

Kinship terms for strangers

A small child addressing an unrelated young man may use this word. A market vendor may call a young customer by the same term to sound friendly. An older woman who is nobody's grandmother is routinely addressed with the word for grandmother, and this is not considered rude in ordinary contexts.

The system estimates a person's position relative to the speaker and applies a family term to it. Age and sex are being read off, which is why the practice can misfire, and Japanese speakers do argue about whether some of these usages have aged badly.

English cannot do this

English kinship terms are reserved for kin, with a few worn-out exceptions. Calling a stranger brother in English signals a specific register, or a subculture, or a joke, and always signals something beyond the words.

English instead reaches for sir, madam, mate or nothing at all, and the nothing at all is telling: English is comfortable addressing a stranger with no term whatsoever, which Japanese finds harder because the sentence usually wants one.

The fandom narrowing

English-speaking fandom associates the word almost exclusively with a particular kind of scene and a particular kind of character, which is a narrow slice of its use. The bulk of its occurrences are entirely mundane: a child getting an older brother's attention at breakfast.

Same mechanism as everywhere else on this site. The dramatic subset travelled, the ordinary majority did not, and the borrowed sense kept the register of the sample rather than of the word.

Quick answers

What does oniichan mean?

Older brother, with the honorific お and the diminutive ちゃん attached. The softest of several forms, the others being oniisan and oniisama.

Is oniichan an insult?

Ordinary and affectionate. It is also used for young men who are not related to the speaker at all, which is the part English does not do.

What does oniichan mean in anime?

Heard from younger sisters and, in fandom, associated with a narrow character type. Its everyday use is far broader and duller.