"assisting, giving support," hence "subsidiary, additional," c. 1600, from Latin auxiliaris "helpful, aiding," from auxilium "aid, help, support," related to auctus, past participle of augere "to increase," from PIE root *aug- (1) "to increase."
c. 1600, "foreign troops in service of a nation at war," from auxiliary (adj.). The Latin adjective also was used as a noun in this sense. In grammar, "a verb used in forming phrases with other verbs and indicating mode or tense," 1762, from the adjective in this sense (1670s). Related: Auxiliaries.