From Latin 'vigil' (awake) — literally 'refusing to sleep,' same root as 'vigor' and 'wake.'
The action or state of keeping careful watch for possible danger or difficulties.
From French 'vigilance,' from Latin 'vigilantia' (watchfulness, wakefulness), from 'vigilāns' (watchful), present participle of 'vigilāre' (to keep awake, to watch over), from 'vigil' (awake, watchful). Latin 'vigil' is derived from PIE *weǵ- (to be strong, lively, alert), a root that also generated Latin 'vegetus' (vigorous, lively), Old English 'wacian' (to be awake, to watch), and ultimately English 'wake,' 'watch,' and 'bishop' (via Greek 'episkopos,' overseer, from the same conceptual field of vigilant guardianship). Vigilance entered English in the 16th century, carrying the military and moral
'Vigilance,' 'vigor,' 'vegetable,' 'wake,' and 'watch' all share PIE *weǵ- (to be strong, lively). Vigilance is staying awake. Vigor is liveliness. A vegetable is something that 'enlivens' (from 'vegetāre,' to enliven). To wake is to become lively. A 'vigilante' is a self-appointed watchman. The same root connects the sleeping guard to the growing garden.