What does Kun mean?

Kun (君) marks someone as junior to the speaker. It is used for boys far more often than girls, but the rule is relative standing, not gender.

Written
(-kun)
Literally
An honorific marking someone as junior to the speaker. Written 君 or in kana as くん; the same character read kimi is an informal word for you.
As slang
Ordinary but directional. It is used downward or between equals and never upward, so addressing a superior this way is a mistake rather than a familiarity.
In anime
Read by fandom as the boys' honorific because school settings supply mostly boys to attach it to. What it actually marks is position, not sex.

Kun marks the person addressed as junior to the speaker. It attaches to boys far more often than to girls, which is why English-speaking fandom reads it as the boys' honorific, but that frequency is a consequence of the rule rather than the rule itself.

The character

Written 君, though it appears constantly in kana as くん. The same character read kimi is an informal word for you, the one used downward or between intimates, and the two uses share a logic: both address someone the speaker is not obliged to elevate.

Direction, not gender

The reliable description is that it points downward or sideways. A teacher uses it for pupils. A manager uses it for junior staff. An older student uses it for a younger one. Nobody uses it for a superior, and the error is not rudeness exactly but a category mistake, like calling a stranger by a nickname.

The gendered reading breaks down in workplaces and universities, where it is normal for a senior figure to address junior colleagues and students of either sex this way. It is less common for women than for men, and it is not unusual.

Why the boys reading took hold

Because of where fandom encountered it. School stories are the dominant setting, classes are addressed constantly, and the pattern presented is boys getting one suffix and girls another, repeated across hundreds of episodes.

From that sample the inference is reasonable. It also strips out the information the suffix actually carries, which is a claim about who stands where.

What it shares with chan

Both encode relationship rather than description, and both operate on a dial the speaker must set before saying a name. Chan measures closeness and this one measures standing, and the two overlap because juniors are often also intimates.

The pairing explains a small thing that puzzles English viewers: why a character switching from one suffix to another, or dropping suffixes entirely, is treated as a significant event. The switch restates the relationship, and doing it unilaterally is a move rather than a habit.

Why English cannot copy it

English marks status with whole constructions rather than with a syllable. Sir, Ms Ito, mate, Dr Ito: each is a separate form of address, and the speaker can dodge all of them by using a bare name.

Japanese offers no comfortable dodge, since the bare name is itself a strong choice. Every utterance containing a name carries a small statement about hierarchy, which is not a thing English requires its speakers to declare, and is why the suffix looks like decoration to people who have never had to pick one.

Quick answers

What does kun mean?

An honorific marking someone as junior to the speaker. Written 君 or in kana as くん; the same character read kimi is an informal word for you.

Is kun an insult?

Ordinary but directional. It is used downward or between equals and never upward, so addressing a superior this way is a mistake rather than a familiarity.

What does kun mean in anime?

Read by fandom as the boys' honorific because school settings supply mostly boys to attach it to. What it actually marks is position, not sex.