A dragon is a mythical monster like a giant reptile with wings. In European tradition the dragon is typically fire-breathing and tends to symbolize chaos or evil, whereas in the Far East it is usually a beneficent symbol of fertility, associated with water and the heavens.
In the show they are much smaller in size than in myths, being shorter than a human. They are an endangered species, and it seems there are only a male and a female left in the world. Each of them live in a zoo, one in New York and the other one London.
In the episode "The Ring of Powers", the female Victoria is on loan from the London Zoo for mating. They must succeed in order to keep from going extinct. Since they both find each other repulsive, Mark Lilly uses the power of influence he got from Leonard Powers' engagement ring to make them copulate.