He is a malevolent xel'naga connected to the Void who engineered a plot to destroy xel'naga and their Infinite Cycle in order to remake the universe in his image.
When the xel'naga began uplifting the zerg, they created the Overmind to control and direct the hive mind, so as to try and avoid the "failure" with the protoss. But the Overmind was not given free will. It was given an overriding directive to obliterate the protoss. Amon had a hand in this. Amon saw the zerg as a valuable tool, appreciating their ability to consume essence from other organisms. He thus bound them to the will of the hive mind, with only the primal zerg escaping his control.
While Amon ultimately planned to eliminate the zerg, he considered the hybrids to be proof of the zerg's success in his greater plan. He intended to enslave the zerg and use them and the hybrids to wipe out the terrans and protoss. Once the hybrids were dominant, he would dispose of the zerg and reshape all life in his own image.
At some point prior to the Great War, Amon ceased to live. However, his influence on the Overmind and the Zerg Swarm still remained, and work on the hybrids still continued.
The Countervailing Pawns
The Overmind was not blind to its plight. It foresaw the apocalyptic outcome if Amon, whom it called "the Fallen One", was victorious. The creation of the Queen of Blades was largely the Overmind's attempt to free the zerg and prevent that future. In the future it glimpsed at, Amon recognized the threat that Kerrigan posed.
Kerrigan was reborn as the Queen of Blades after Amon's death. Because of this, while she still felt his lingering influence over her, and had her personality twisted, she was effectively an individual, as opposed to the Overmind.
Four years after the Overmind's death, Tassadar, now in spirit form, passed on the creature's vision to Zeratul, who made sure to warn Jim Raynor of Kerrigan's importance and to ensure her survival. Zeratul wondered if Amon (who he only knew as the Fallen One at the time) was a xel'naga. Regardless, Raynor followed through, and successfully de-infested Kerrigan on Char through a xel'naga device, freeing her of Amon's taint.
After returning to the Koprulu Sector, Kerrigan was contacted by a resurrected Alexei Stukov, now an infested terrain. He pointed her to Skygeirr Platform, which was producing hybrids under the direction of Doctor Emil Narud. Kerrigan and her forces fought her way through the station, defeating Narud's forces which included Dominion troops, Hybrids, and Tal'darim protoss. Eventually, she found her way to the xel'naga temple beneath it. There, she battled Narud, revealed as a servant of Amon. Kerrigan defeated Emil Narud the shapeshifter, but in his last moments, Narud revealed that Amon was alive and would be returning soon.
Although Kerrigan nearly died, she was able to glimpse into Narud's mind before he died as well. Having initially assumed that Amon was permanently dead, she discovered that he was in fact alive. She realized that after killing Mengsk, she would have to face Amon one day, as somehow, Narud was successful in resurrecting him. After defeating Mengsk on Korhal, she departed to do battle with Amon.
Reflecting on her fight with Narud, Stukov speculated that the xel'naga device used to de-infest Kerrigan may have actually had a hand in somehow reviving Amon. He noted that the original Queen of Blades had tremendous power and that the device couldn't just simply erase it, surmising that it had to "go somewhere."