We owe this word to the Roman writer Horace, who wrote in his Ars Poetica (The Art of Poetry): “Proicit ampullas et sesquipedalia verba” (“He throws aside his paint pots and his words that are a foot and a half long”). It comes from Latin sesqui–, one and a half, plus ped, a foot. It was borrowed into English in the seventeenth century to refer to a long word or to a person who is known for using long words and has become a favourite of those writers who like self-referential terms, or are addicted to polysyllabic humour.
It appears, somewhat disguised, in The History of Mr Polly by H G Wells: “Words attracted [Mr Polly] curiously, words rich in suggestion, and he loved a novel and striking phrase. His school training had given him little or no mastery of the mysterious pronunciation of English, and no confidence in himself... He avoided every recognized phrase in the language, and mispronounced everything in order that he shouldn’t be suspected of ignorance but whim. ‘Sesquippledan,’ he would say. ‘Sesquippledan verboojuice.’ ”
Somebody who uses long words is a sesquipedalianist, and this style of writing is sesquipedalianism. The noun sesquipedality means “lengthiness”. If such words are not enough, there’s always hyperpolysyllabicsesquipedalianist for someone who enjoys using really long words.