The answer I think you are seeking is this, as far as I remember it. For more detail, search the Merlin/Arthur/Celtic myths. Merlin was supposed to have been born of a woman without the intervention of a man. I don�t remember why this was, but it was to do with defeating Mab, the Queen of the Faeries. This is what gave him his magical powers. There was an ancient king, Vortigan (who I believe was a historical figure) who wanted a castle built, but all efforts resulted in failure. The castle always fell down before completion. His magical advisors told him he must sacrifice a boy who had no father. Enter Merlin. Merlin, to save his life said he could tell Vortigan how to build his castle. He was spared and Merlin told him that beneath the foundations was a pool in which there were two dragons, one white, and one red. He must uncover the pool, allow the dragons to fight and if the red dragon won, the castle would stand. If the white won, the castle would always fall. Of course, the red dragon won, Merlin was spared and the red dragon became Vortigans symbol. Vortigan betrayed the English (who we know are really the Welsh, forced to the west of what was then a Celtic Albion) to the Norsemen and he was in turn betrayed and killed by the Norsemen. The red dragon became the Welsh National flag.
While I may have made some historical and mythical errors, this is the gist of the myth and the reason the red dragon is the symbol of Wales. I hope this is what you were after.