Elijah is an original vampire. He is Klaus' brother, and despises Klaus for killing his family. Being an original, Elijah has the ability to compel other vampires.
He makes a deal with Elena, and tells her that as long as she stays put, he would not harm her friends or family.
Right as Bonnie is about to kill Klaus at the end of season 2, Klaus tells Elijah that he can reunite him with his family if he saves him. In an act of desperation, Elijah breaks his word to Elena by saving Klaus.
In the end, Klaus reunites Elijah with his family....by kidding him with the white oak ash dagger.