"Illuminate" traces back to Latin illuminare — "to light up, make bright" — a combination of the prefix in- ("upon") and lumen ("light"). English got hold of this word around 1500, either as a shortened form built from "illumination" or borrowed directly from the Latin past-tense form illuminatus. That's why it still looks so Latin: the spelling with the double "l" and the "-ate" ending reflects its Roman roots pretty directly, without much English mangling along the way.
But English actually had an older way of expressing a similar idea before "illuminate" showed up. Back in the late 1300s, people used the word "enlumyen," borrowed from Old French "enluminer," meaning to decorate handwritten manuscripts with gold, silver, and bright colors — think of the beautifully decorated capital letters in medieval books. That word also traces to the same Latin root, just filtered through French first. Around the same time, English also used "illumine" for similar meanings.
Once "illuminate" arrived around 1500, it originally meant simply "to light up" or "shine on," especially in a lavish way. By the 1530s, it took on the specific sense of decorating a place with lots of lights, especially for a festival or celebration. Then, by the 1560s, people started using it figuratively too — to mean "to enlighten" or "to inform," much as we still say someone "illuminates" a difficult subject today. Over time, the practical, physical meaning (lighting up a room) and the metaphorical meaning (lighting up the mind) settled comfortably together in this one Latin-rooted word.
illuminate (v.) c. 1500, "to light up, give light to, shine on," especially "to light up profusely," a back-formation from illumination or else from Latin illuminatus , past participle of illuminare "light up, make light, illuminate." Earlier was enlumyen (late 14c.) "decorate written material by hand with gold, silver, or bright colors," from Old French enluminer , from Late Latin inluminare ; also illumine (late 14c.). As "give light to, decorate with many lights," 1530s, especially "light up (a place) profusely as for a festival." As "enlighten, inform" 1560s. Related: Illuminated ; illuminator ; illuminating ; illuminable; illuminant . also from c. 1500