Douglas Harper's Etymology Dictionary
chief character in two popular books by English writer John Lyly (1553-1606), from Greek euphyes "well-endowed by nature." The affected and ornate style of writing and speech popularized by the works was fashionable late 16c.-early 17c.; hence euphuism (1590s); euphuistic; euphuist.
Wikipedia
Euphues: The Anatomy of Wyt , a didactic romance written by John Lyly, was entered in the Stationers' Register 2 December 1578 and published that same year. It was followed by Euphues and his England, registered on 24 July 1579, but not published until Spring of 1580. The name Euphues is derived from Greek meaning "graceful, witty." Lyly adopted the name from Roger Ascham's The Scholemaster, which describes Euphues as a type of student who is "apte by goodnes of witte, and appliable by readines of will, to learning, hauving all other qualities of the mind and partes of the bodie, that must an other day serue learning, not trobled, mangled, and halfed, but sounde, whole, full & hable to do their office" (194). Lyly's mannered style is characterized by parallel arrangements and periphrases.
The style of these novels gave rise to the term euphuism.