1590s, "power to accomplish something," from Latin efficientia "efficient power; efficiency; influence" (from efficientem; see efficient) + -cy. In mechanics, "ratio of useful work done to energy expended," from 1858. Attested by 1951 as short for efficiency apartment (itself from 1917).
she did the work with great efficiency
effervescence
effervescent
effete
efficacious
efficacy
efficiency
efficient
effigy
effleurage
effloresce
efflorescence