The dragon is a legendary serpent-like creature from the myths of Europe and China on Earth.
There is also a real animal known as a dragon on Berengaria VII. Spock saw one when he visited the planet. (TOS: "This Side of Paradise") A Vulcan survey team had made note of the species as one of flying reptiles, over 200 meters in length, that breathe fire. (ENT: "Bound")
Dragons are sometimes use as symbolism to express an idea. The Vaadwaur stasis units were compared to dragon's teeth. (VOY: "Dragon's Teeth") And The Doctor compared Qatai's quest to kill the Telepathic pitcher plant to dragon slaying. (VOY: "Bliss")