This adjective has no flavour of modern vegetables: it is a word used mostly to describe a person: someone who is vigorous, vital, vivid, vivacious, who may well be vigilant—but who presumably like other mortals needs his or her victuals.
It is also used to describe a person’s mind or intellect: Cicero talks about the quality of a mens vegeta (Tusc. Disp. I.17); and Livy in philological mood says of Camillus, who in old age was chosen as commander-in-chief in the war against the Volsci:
exactae iam aetatis Camillus erat… sed vegetum ingenium in vivido pectore vigebat virebatque integris sensibus… (Book VI.22)
Charlton T. Lewis* in his Elementary Latin Dictionary (1891), which is more than elementary, suggests that the southern European root for these words was VIV- or VIG- and that goes for βίος, earlier γϝίϝος.
In the Germanic languages this root was something beginning WA-, as in wake, watch and wait.
In the Yorkshire town of Ripon, the town hall bears an inscription saying that, ‘Except the Lord keep the cittie the Wakeman waketh in vain’: for in that town the Mayor was called the Wakeman until the 17th century.
English has three nouns for something but with different connotations—which students may be invited to distinguish—a watch, a wake, and a vigil.
English borrowed the word vegetable from French in the Middle Ages: an adjective to denote something alive and thriving. It eventually—in English— came to mean something alive but not animal, and from that came its modern meaning—which is not the case in French, for their word is légume.
But French now has the word végétarien, borrowed from English—which may be an irritation to the Academie Française.
* co-editor of Charles Short.