Doublets occur when a word from another language is borrowed into English more than once, leaving two distinct forms. Once a borrowed word arrives in English, it's subject to all the sound changes that the native words undergo: just as the native word my stopped being pronounced "me" around 1450, so the borrowed word sky stopped being pronounced "ski". (What did English use for the blue object that's overhead when we're outdoors, before borrowing sky back in the days of the vikings? Why, heaven, which can still be used that way but is mostly used in a more specialized meaning now.)
A fine example of a doublet is gentle and genteel, which are both borrowings from French gentil. The former arrived with the big wave of French words between the Norman Conquest and Chaucer's day, and is first recorded in writing in the early 13th century; the latter was borrowed in the late 16th century, well after the Great Vowel Shift and before the final standardization of English spelling in the 18th century.
But wait, there's more! There is also jaunty, which is an offshoot of genteel that came to have a meaning of its own. All of these words originally meant "noble, well-bred", as the French original did, but shifted meaning in various ways: gentle toward "soft, mild"; genteel toward "courteous, elegant"; jaunty toward "lively, brisk" — all supposed attributes of the nobility. Finally, gentil itself descends from the Latin adjective gentilis, meaning "belonging to the same clan or nation"; from this word we get English gentile, a non-Jew (or in Mormon country, a non-Mormon, Jewish or not).
Amazing enough for you? Consider the Latin word discus, which gives us five English words: discus itself; disk or disc, a shortened form of it; dish, which arrived before the Conquest and underwent the sound-change that converted all "sk" into "sh" (later "sk" words are borrowings, like Norse skirt next to native shirt); dais, which arrived in Middle English from French; and lastly desk, also arriving in Middle English, but from Italian. Latin discus is itself a borrowing from Greek ....
A few more: inch direct from Latin uncia (one-twelfth) back in Old English days, ounce also from uncia via French (originally pounds had twelve ounces only, and still do when you talk of gold or silver); canal straight from Latin as-is, channel via French; captain from Norman French, chieftain from Parisian French; shabby from the native English wordstock, scabby from Old Norse.