Harkon was once a king of a vast and powerful domain. However, he feared that his mortality would hinder him from gaining power. So he decided to pledge himself to Molag Bal and sacrificed a thousand people in his name. In return, Molag Bal granted him immoratlity by turning him and his family into vampires.
As the years passed, Harkon discovered a prophecy called the "Tyranny of the Sun." If this prophecy was enacted, it would blot out the sun and allow his fellow vampire to roam around Skyrim freely. He became so obsessed with this prophecy, so much so that he was willing to push aside everything in his life, including his family, to fulfill it.
To enact the prophecy, he needed Auriel's Bow and the blood of a Daughter of Coldharbour, namely his daughter, Serana. His wife, Valerica, saw what Harkon was trying to do and sought to put an end to it. She thought that if vampires could roam freely, they would be too out in the open. She thought that this would lead to the ultimate extinction of vampires.
In order to put a stop to Harkon's goals, Valerica decided to lock Serana and an Elder Scroll inside Dimhollow Crypt for her protection. Valerica decided that she would would go hide in the Soul Cairn, a plane of existence where used souls of soul gems go to. Harkon became enraged by what happened and ordered every vampire to scour the continent to find Serana. But after centuries had gone by, Harkon lost hope.
Harkon is often seen as an elitist who believes that mortal beings are beneath him. He has little to now care for his family. The only reason he remembers his family is because he sees his daughter as a means to obtain more power. Harkon also shows tremendous cruelty, allowing nothing to stop him on his quest for domination. He views other vampires found in Skyrim to be nothing more than feral animals who only frighten the mortal citizens that he and his pure-blooded vampires feed upon.
Harkon shows a great deal of hatred towards his wife, Valerica. He wishes to gain revenge against her for betraying him and halting his plans. He also shows a similar hatred towards werewolves, whom he sees as filthy animals more than anything.