late 15c., "to use to one's profit, to increase (income)," from Anglo-French emprouwer "to turn to profit" (late 13c.), from Old French en-, a causative prefix or from em-, + prou "profit," from Latin prode "advantageous" (see proud (adj.)).
Spelling with -v- was rare before 17c.; it apparently arose from confusion of -v- and -u-. Spelling otherwise deformed by influence of words in -prove. Meaning "make better, raise to a better quality or condition" first recorded 1610s. Intransitive sense "get better" is from 1727. Phrase improve the occasion retains the etymological sense. Meaning "to turn land to profit" (by clearing it, erecting buildings, etc.) was in Anglo-French (13c.) and survived or was revived in the American colonies and Australia. Hence, "make good use of, occupy (a place) and convert to some purpose."