If someone tells you that you have refulgent eyes, they mean that your eyes shine brightly, like the stars. This suggests that your special someone is the poetic type, since refulgent is a literary way of saying "bright."
The adjective refulgent comes from the Latin fulgere, meaning "to shine." Refulgent is used both literally and figuratively. On a bright day, the sun can be described as refulgent, and the beautiful, sunny weather might cause you to break into a refulgent smile. Refulgent shines brightly among its synonyms: radiant, dazzling, and luminous. You'll typically encounter refulgent in literature and poetry, but using this word is a great way to show off your refulgent mind.