early 15c., "that which moves the mind or stirs the passion," from Late Latin incentivum, noun use of neuter of Latin adjective incentivus "setting the tune" (in Late Latin "inciting"), from past participle stem of incinere "strike up," from in- "in, into" (from PIE root *en "in") + canere "to sing" (from PIE root *kan- "to sing"). The sense apparently was influenced in Late Latin by association with incendere "to kindle." (Milton uses the adjective to mean "setting fire, incendiary.") Meaning "rewards meant to encourage harder work" is from 1948, short for incentive payment, etc. (see incentive (adj.)).
c. 1600, "provocative, exciting, encouraging," from Late Latin incentivus "inciting" (see incentive (n.)). In reference to a system of rewards meant to encourage harder work, first attested 1943 in jargon of the U.S. war economy.