Akihiko Kayaba is the Director and Creator of the Nerve Gear and Sword Art Online. He traps all the players within Sword Art Online by using the Nerve Gear to cease sending signals to the users' body. Any attempt at removal, loss of power for a certain period, or if the user dies in the game will also kill the user. His motivation is to observe what happens after he traps them.
He is in fact Heathcliff in the game SAO, who is the leader of the guild Knights of Blood. This was found out and revealed by Kirito after the defeating of the boss on the 75th floor. Because of this, he offered Kirito a chance to beat him in the duel with the condition that if Heathcliff is defeated, the remaining players will be able to log out. After a fight in which it appears both Kirito and Asuna are defeated and killed, Kirito, with his final efforts, managed to use Asuna's rapier and stab Heathcliff through the chest thus defeating him and clearing the game. It was later revealed that neither Kirito nor Asuna died and in the final moments of the game Heathcliff personally congratulated Kirito on winning the game, saying that he was the one he had an eye on from the beginning due to his amazing reflexes and reaction time which granted him the use of <Dual blades>. He then faded away along with the virtual world he created
In the closing moments of the ALO incident when it appeared Sugou had defeated Kirito and Asuna due to his GM status, Kayaba reveals himself with a even higher status as the game's creator (ALO was made from a copy of the SAO server) and allows Kirito the chance to have a fair fight with Sugou in which he easily wins thus recusing Asuna. Kayaba then gave Kirito a "seed" which he said that he leaves its fate to his hands. Whether to delete or forget it is fine, but if he did have some lingering emotions for Aincrad then he would ask Kirito to let it bloom.
It was revealed in the aftermath of the ALO incident that Kayaba is indeed dead, his body found five months after the game was cleared. Before his death however he scanned his brain with the success rate being very very low, but he was apparently successful but it burned his brain resulting in his death. This copy of himself was the one that helped Kirito when he was fighting Sugou