The flare of protective affection a character design triggers; also the industry built on triggering it.
Documented
The sprout, or the fire
Moe is the verb moeru, to bud or sprout, applied since 1990s message-board culture to the surge of feeling for a character. The homophone moeru, to burn, was noticed immediately, and the community itself has never settled whether affection sprouts or ignites.
Assessment: The origin dispute is itself documented, which is rare: a word whose etymology fight is part of its record.
Stories
The board wars of a feeling
The story: on the 1990s forums, fans needed a word for the jolt, this character, this exact combination, and moe rose out of the threads. Tiny wars were fought over the spelling, the source, the meaning. Nobody won; the word escaped and got an industry named after it anyway.
Assessment: Documented as genuine online etymology debate. The most honest thing about the word is that its parents are still arguing.
Interesting claims
Affection by database
The critic Azuma Hiroki's claim: moe is love detached from story, response trained to elements pulled from a database of parts, the otaku heart animalized, reacting to cat ears the way an animal reacts to a stimulus. On this reading moe is not a feeling discovered but a reflex farmed.
Assessment: Azuma's database-consumption thesis is documented scholarship with real influence. Whether it is a diagnosis or just a description is still being fought over, which may prove the thesis.
Sources and further reading
1990s BBS and forum archives, the sprout-versus-burn debate
Azuma Hiroki, Otaku: Japan's Database Animals
Standard dictionaries, moeru, to bud, and moeru, to burn
Worth asking
If affection can be engineered from a list of parts, cat ears, glasses, clumsiness, was it affection at all?