late 14c., "formal authorization, official permission, permit, privilege," from Old French licence "freedom, liberty, power, possibility; permission," (12c.), from Latin licentia "freedom, liberty; unrestrained liberty, wantonness, presumption," from licentem (nominative licens), present participle of licere "to be allowed, be lawful," from PIE root *leik- "to offer, bargain, make a bid" (possibly source also of Lettish likstu "I come to terms").
Meaning "formal (usually written) permission from authority to do something" (marry, hunt, drive, etc.) is first attested early 15c. Meaning "excessive liberty, disregard of propriety" in English is from mid-15c. In Middle English spelled licence, licens, lisence, lissens, licance. There have been attempts to confine license to verbal use and licence to noun use (compare advise/advice, devise/device, and see note in OED).
Poetic license "intentional deviation from recognized form or rule" is from 1733, earlier as lycence poetycall (1530). The licence-plate is from 1870 (of dogs and wagons before automobiles); licence-number is by 1903.