Klaus is a werewolf/vampire Hybrid. This means, along with being an original vampire, Klaus is also a werewolf. He is the half brother of Elijah and is the reason that vampires and werewolf believe there is a sun and moon curse. In actuality, Klaus is the only one who has been cursed by an Aztec shaman because he is both a vampire and werewolf.
He met Katerina Petrova (Katherine) in the late 1400s, and plans to sacrifice her to break the curse. He has to use Katherine as the sacrifice since it was the sacrifice of her ancestor that was used in the creation of the curse.
She became a vampire when trying to escape him. When he finds out about Elena's existence, he becomes obsessed with her and plans on using her for the sacrifice. Along with forcing Katherine to turn her Aunt Jenna into a vampire as a sacrifice.
Season 2 ends with Bonnie nearly killing Klaus, but Elijah stopping it when he finds out the he can bring back his family if he saves Klaus.
He's your first love. I intend to be your last. However long it takes.Klaus [to Caroline]
You build your army so big that no one will dare pick a fight.Klaus