In plural, the Greek word could mean "one's own countrymen." In old English law, one who has been without reasoning or understanding from birth, as distinguished from a lunatic, who became that way. Idiot box "television set" is from 1959; idiot light "dashboard warning signal" is attested from 1961. Idiot savant attested by 1870.
"clasp, button, etc. used to secure the cock of a hat," hence "any knot or badge worn on a hat," especially as a sign of political adherence, 1709, earlier cockard (1650s), from French cocarde (16c.), fem. of cocard (Old French cocart) "foolishly proud, cocky," as a noun, "idiot, fool;" an allusive extension from coq (see cock (n.1)).