mid-14c. variant of lorrer (c. 1300), from Old French laurier, lorier "bay tree, laurel tree" (12c.), from Latin laurus "laurel tree," which is probably related to Greek daphne "laurel" (for change of d- to l- see lachrymose), which is probably from a pre-IE Mediterranean language.
The second -r- changed to -l- in late Middle English by dissimilation. An emblem of victory or of distinction, hence the phrase to rest (originally repose) on one's laurels, first attested 1831. Related: Laurine (adj.).