The primary driver of his will is Goku. Vegeta's defeat in his first encounter with Goku and his unwillingness to accept Goku being more powerful had constantly fuelled his strong will to continue to train himself. After seeing Goku turn into Super Saiyan and defeating Frieza, he grew even more jealous of Goku's achievements and immersed himself in intensive training. After much sweat and frustration, he finally became Super Saiyan. He only enjoyed a fleeting moment of pride in destroying #19, before being defeated by #18.
Vegeta's first catharsis occurred during Gohan's battle with Cell. Because of his rash decision to attack Cell when he did not have the power to, he caused Gohan's arm to be seriously injured when Gohan saved his life. Not only was he not even close to Cell's ability, but also served as a hindrance to Gohan. That was the first time Vegeta accepted his incapabilities by making an apology to Gohan.
By the time Majin Buu appeared, what used to be a cold-hearted Vegeta changed. Right before he proceeded to sacrificed his life to destroy Buu, he told Trunks that he cared about him and how he felt bad about giving Trunks much less attention then Trunks deserved.
During Goku's final battle with Majin Buu, Vegeta goes through a complete catharsis. He realized that Goku's pure and kind heart gave Goku the power that Vegeta never had. He finally realizes that the good ultimately prevails.
Later on, Vegeta and Bulma have a daughter named Bra.
