c. 1200, onur, "glory, renown, fame earned," from Anglo-French honour, Old French onor, honor "honor, dignity, distinction, position; victory, triumph" (Modern French honneur), from Latin honorem (nominative honos, the form used by Cicero, but later honor) "honor, dignity, office, reputation," which is of unknown origin. In Middle English, it also could mean "splendor, beauty; excellence." Until 17c., honour and honor were equally frequent; the former now preferred in England, the latter in U.S. by influence of Noah Webster. Meaning "feminine purity, a woman's chastity" first attested late 14c. Honor roll in the scholastic sense attested by 1872.
The initial h in honest, honor, etc., is merely etymological, the sound having already disappeared when the word came into ME use. [Century Dictionary]
It was a Latinate correction that began to be made in early Old French. From c. 1300 as "action of honoring or paying respect to; act or gesture displaying reverence or esteem; state or condition inspiring respect; nobleness of character or manners; high station or rank; a mark of respect or esteem; a source of glory, a cause of good reputation." Meaning "one's personal title to high respect or esteem" is from 1540s.