I have retold this story in my own words - feel free to tell it in yours.
In the turmoil of the end of the Roman Empire in the west, when the Romans abandoned Britain to her enemies, and heathen pirates descended from all sides like ravenous wolves, from Ireland and Germany alike, there arose many tyrants in Britain, and one of these was Vortigern, Gwrtheyrn in Welsh, meaning High King. He it was who invited two Saxon chiefs, Hengist and Horsa, to Britain to defend this country, and gave them Kent to settle.
But then he grew besotted with Hengist's daughter Rowena, and invited all his chief men, Britons and Saxons together to a great feast held at Stonehenge, but Hengist betrayed him, for he and his men brought their long knives with them, (the seax which gave the Saxons their name). When everyone was half-drunk, the Saxons massacred all the British chiefs, sparing only Gwrtheyrn, and from then on there was war between the Britons and the Saxons. That was the original "Night of the Long Knives".
Gwrtheyrn fled to the mountains of North Wales, and chose a strong place to build himself a fortress, for he was as afraid of the Britons as of the Saxons; But however much was built during the day, in the morning it lay on the ground in ruins. So Gwrtheyrn summoned his wise men and demanded that they solve the mystery, and after they had huddled togther in a corner and pored over their books and shouted and argued, they came up to the king and announced that what was needed was to find a boy who didn't have a father, and to sprinkle his blood over the rock.
This didn't sound very promising, but Gwrtheyrn was the king so he sent his messengers throughout the country, and it so happened that one of them came to Caerfyrddin (Carmarthen in English) and overheard two boys squabbling and fighting, "you can talk, you haven't got a father". Then he found the boy's mother, who was the king's daughter, and she swore that it was true, that she'd never known a man but had been visited by a demon in the night, an incubus.
So the boy, Emrys, was brought back to Gwrtheyrn and brought before the king, and his story told to the king. But the boy asked what the king had been told, and then he poured scorn on the advisors as ignorant greybeards, and asked them what was below the rock - they didn't know. So he said that there was a hollow cave, and when the workmen dug down they found a cave. And at the bttom of the cave was a rock and he asked the advisors what was under the rock, and of course they didn't know.
And Emrys declared that there were two dragons, two worms, beneath the rock, and that it was their fighting which shook the rock in the night so that the castle fell down. And when they moved the rock, sure enough there were the two dragons, one red and one white and they started fighting before the king and all his court; all the rock shook and Gwrtheyrn trembled as he watched, but Emrys stood still. At first the white dragon appeared to be winning, but at last the red dragon stood triumphant, and the white dragon fled to the east.
"W-what does that mean," quavered one of the advisors. Then Emrys declared that the white dragon represented the Saxons and the red dragon the Britons, and that they would fight for many years; but although the Saxons would win for a while, in the end the Britons would drive them into the sea. "But woe to the man who brought them into this country," he said turning to Gwrtheyrn.
Then the king rose and fled to the valley later known as Nant Gwrtheyrn after him, and according to some he built his house there and died when it was struck by lightening, but according to others he leapt into the sea, at a rock still called Carreg Llam, the Rock of the Leap.
Source of the Story
In the earlier version recorded by Nennius, this boy is Ambrosius who later defeated the Saxons at the Battle of Mount Badon, but according to Geoffrey of Monmouth he was Merlin Ambrosius (in Welsh, Myrddin Emrys), and Caerfyrddin was popularly supposed to be derived from Caer + Myrddin (n fact the second element is from the Romano-British name Maridunum, sea-fort).
Y Ddraig Goch - The Red Dragon
Since then the Red Dragon, Y Ddraig Goch, has been a symbol to the Welsh, and a reminder that they will be free in the end. The motto "Y Ddraig Goch ddyry cychwyn" means something like "the Red Dragon leads the way", and comes from a poem written by a bard to his patron as thanks for the gift of a bull; in the words of the Western Mail, "it refers to a certain part of the bull's anatomy, and what he does with it"
See also: The British History Pages