Sir Arthur Dayn, the knight whom Eddard Stark called "The finest knight I ever saw was Ser Arthur Dayne, who fought with a blade called Dawn, forged from the heart of a fallen star." He was famed for his prowess and his chivalrous and kind heart.
Arthur Dayne was the deadliest Kingsguard of Aerys II the mad king (father of Rahegar, Viserys and Daenerys the mother of Dragons.) He carried a greatsword, called Dawn, milky white and made out of a meteorite. It is not made of Valyrian steel, but it is thought to be as strong and sharp.
He was a friend and close campaign of Rahegar, the Crown Prince who was killed by Robert Baratheon at the trident, in his revolt against the Targaryens.
Finally, Ser Arthur Dayne was killed at the tower of Joy, and his sword was returned to his sister. His fate, why he was there and not at the battle of the trident is of critical importance to our story. However, i will leave that for the show to reveal...
The Great Sword Dawn is currently in the ancestral home of the Daynes, far south close to Dorn, and is awaiting the next worthy knight to hold it and become the next "sword of the morning". The only Dayne we came across in GOT is the young squire Edric Dayne, who is with the brotherhood without Banner.
For more info check these pages (some spoilers, especially about the death of Dayn)