For all the chapters of the manga and for all the episodes of the TV series, there are speculations about Seto's past, but it's totally revealed only in the last part of the story, the one related to the Pharaoh's Memories. Kaiba never believed to Atem's words about their past lives, but when he went in Egypt, he realized that he really was the High Priest Seth, the major priest beside the Pharaoh.
Seto was Atem's cousin but he didn't know it because his father, Aknadin, hid him the truth. Seth's job was to find powerful "KA" (men or women with special souls) in order to use them to protect the Pharaoh and fight against his enemy, Zorc.
BLUE EYES WHITE GIRL
One of these Ka was Kisara, a beautiful and sweet girl called "Blue Eyes White Girl" from the people because she had blue eyes and white hair but in realty she owned the Blue Eyes White Dragon's Soul. Seth was very impressed of her, she wasn't only a Ka but a special girl that felt in love with him since the first time they met, some years ago, when Seth wasn't yet a priest and helped her to escape from someone who wanted to kill her.
Kisara never forgot about him and when they met again, Seth rescued her for the
second time. Kisara's influence changed Seth's heart from the bottom, he became sweeter and happier. But Seth's father, Aknadin, never approved their relation and he killed Kisara in order to obtain the Blue Eyes White Dragon's power hidden inside of her.
AGAINST HIS FATHER
After Kisara's death, Seto becomes mad and fights only for himself and his revenge. He fights against Aknadin but after Aknadin's suicide, Seth's soul is possessed by him. With his son's body, Aknadin challenges Atem, but he understands Seth's change and fights to rescue his soul. During the battle, Kisara's spririt protects Seth and brings back his soul, freeding him by Aknadin and Millennium Road's influence.
So, in order to protect Seth and the others and defeat Zorc, Atem sigilled the Millennium Items' power and closed himself in the Puzzle, declaring Seth as his successor, the new pharaoh. But that battle never had an end and the stone with its draw is remembered and on showed in the museum.
5000 years after, Seth and Atem relives in Seto and Yugi and their rivalry and friendship are shown again, in different lives but similar souls. Seto's feelings and rage derives from his past too, and when he accepts the realty, at the and of the story, finally he can live free from the obsessions of the past. So, even if he always says that he's the duelist n.1, now he can admit that the best among all is Yugi. This revelation of his thought doesn't change his desire to beat him and to be the n.1 again.