Klaus's redemption is ultimately what launches The Originals, and it's his love for his daughter, Hope, that is the key to his redemption. She's the light to his darkness. For over 1000 years, Klaus viewed love as a weakness. At first, he doesn't even care about his daughter. But then, she's born and everything changes. Hope shows Klaus the power of unconditional love. She loves him unconditionally and never judges him. And in return, he works to become a better person for her. That's why it's fitting that he finds freedom from immortality by sacrificing his own life to save her, perhaps giving him a real chance at happiness. Klaus's redemption coming in sacrifice for love and in believing he was loved gave the series full-circle symmetry.