The Latin suffix is cognate with Greek -inos/-ine/-inon, and in some modern scientific words the element is from Greek. Added to names, it meant "of or pertaining to, of the nature of" (Florentinus), and so it also was commonly used in forming Roman proper names, originally appellatives (Augustinus, Constantinus, Justinus, etc.) and its descendants in Romanic languages continued active in name-forming. The Latin fem. form, -ina, was used in forming abstracts (doctrina, medicina). Relics of the attempt to continue a distinction between Latin -ina and -inus account for the English hesitation in spelling between -in and -ine.
word-forming element making nouns of quality, state, or condition, from Middle English -our, from Old French -our (Modern French -eur), from Latin -orem (nominative -or), a suffix added to past participle verbal stems. Also in some cases from Latin -atorem (nominative -ator).
In U.S., via Noah Webster, -or is nearly universal (but not in glamour), while in Britain -our is used in most cases (but with many exceptions: author, error, tenor, senator, ancestor, horror etc.). The -our form predominated after c. 1300, but Mencken reports that the first three folios of Shakespeare's plays used both spellings indiscriminately and with equal frequency; only in the Fourth Folio of 1685 does -our become consistent.
A partial revival of -or on the Latin model took place from 16c. (governour began to lose its -u- 16c. and it was gone by 19c.), and also among phonetic spellers in both England and America (John Wesley wrote that -or was "a fashionable impropriety" in England in 1791).
Webster criticized the habit of deleting -u- in -our words in his first speller ("A Grammatical Institute of the English Language," commonly called the Blue-Black Speller) in 1783. His own deletion of the -u- began with the revision of 1804, and was enshrined in the influential "Comprehensive Dictionary of the English Language" (1806), which also established in the U.S. -ic for British -ick and -er for -re, along with many other attempts at reformed spelling which never caught on (such as masheen for machine). His attempt to justify them on the grounds of etymology and the custom of great writers does not hold up.
Fowler notes the British drop the -u- when forming adjectives ending in -orous (humorous) and derivatives in -ation and -ize, in which cases the Latin origin is respected (such as vaporize). When the Americans began to consistently spell it one way, however, the British reflexively hardened their insistence on the other. "The American abolition of -our in such words as honour and favour has probably retarded rather than quickened English progress in the same direction." [Fowler]