What does 馬鹿 Baka mean?

Baka means fool. How offensive it is depends on who says it, to whom, and in what tone, and the range runs from genuine contempt to something close to a term of endearment.

The characters are a red herring

馬 is horse and 鹿 is deer, which has produced a great deal of confident nonsense online about the phrase meaning someone who cannot tell a horse from a deer. The characters are almost certainly ateji: kanji chosen to supply the sound rather than the sense.

There are competing accounts of the actual origin. One traces it to the Sanskrit moha, meaning delusion or folly, arriving through Buddhist vocabulary. Another connects it to a story in Sima Qian's Records of the Grand Historian in which the official Zhao Gao presents a deer and calls it a horse to identify which courtiers will contradict him. Neither is settled. The honest position is that the writing came after the word and nobody is certain what the word came from.

How hard it actually lands

Weaker than English speakers assume. It is not profanity. A parent says it to a child, friends say it to each other, and it appears in ordinary conversation without anyone flinching. Regional weight varies: in the Kansai area aho occupies the affectionate slot and baka is the sharper of the two, while in Tokyo the relationship reverses.

Compounds tune it further. 馬鹿野郎 (bakayarou) is a real insult. 馬鹿正直 (baka-shoujiki) means honest to a fault and is close to a compliment. The root is flexible in a way that English idiot is not.

What fandom did to the calibration

English speakers overwhelmingly met this word in one context: a flustered character, usually a tsundere, saying it while looking away. That is a specific comedic register, and meeting a word only in its comedic register leaves you with no sense of its neutral one.

The result is that baka is simultaneously the word most English-speaking fans know and the one they are most likely to misjudge. Used sincerely, to a stranger, in the wrong tone, it is rude. Used the way anime taught it, it is a joke about a character being unable to admit affection.

Why it travelled so well

Short, percussive, and instantly attached to a memorable delivery. Loanwords that spread through fiction tend to be the ones with a performance attached rather than the ones that fill a gap in the language: English has no shortage of words for fool. What it did not have was that particular two-syllable sound, said in that particular way, by that particular kind of character.