In ancient Athens, an idiōtēs was a perfectly respectable kind of person: a private citizen, as opposed to a public official or someone active in the running of the state. The word came from idios ("one's own, private, peculiar to oneself") and originally meant nothing worse than "minding his own business."
A City That Valued Public Life
The shift happened because Athens valued political participation so highly. To be an active citizen — to attend the assembly, to serve on juries, to argue policy — was the mark of a full member of the community. To remain a private person was to be uninvolved, uninformed, and somewhat suspect. Greek writers began using idiōtēs to mean an amateur or unskilled person; later still, an ignoramus.
Through Latin to English
Latin idiota took on the broader sense of "untrained person, layman" — particularly someone not learned in Latin. Medieval English borrowed the word in this sense before it slid further down the slope toward "fool" or "imbecile" by the late Middle Ages. By Shakespeare's time, "idiot" had its modern dismissive meaning.
An Embedded Political Argument
The original Greek meaning of "idiot" carries a political argument that some modern writers have tried to reactivate. To be private — to have no interest in public affairs — was, the Athenians thought, a kind of failure. The word 'idiosyncrasy', also from idios, preserves the older neutral sense: a peculiarity, something private to a person, with no implication of stupidity. The two words are siblings, and idiosyncrasy is the one that kept its original meaning.