As a girl, Cersei Lannister visited a fortune teller with a friend and the witch accurately predicted the death of Cersei's friend, and later Cersei's marriage to Robert. Because of that Cersei was terrified of her own prophecy, which also predicted that she would become queen only to be replaced by a younger and more beautiful woman, that she'd live to see all of her children perish, and that she'd be killed by the valonqar. (Valonqar is Valyrian for little brother).
Cersei: When will I wed the prince?
Maggy: Never. You will wed the king.
Cersei: I will be queen, though?
Maggy: Aye. Queen you shall be... until there comes another, younger and more beautiful, to cast you down and take all that you hold dear.
Cersei: Will the king and I have children?
Maggy: Oh, aye. Six-and-ten for him, and three for you. Gold shall be their crowns and gold their shrouds. And when your tears have drowned you, the valonqar shall wrap his hands about your pale white throat and choke the life from you.
Cersei believes the prophecy is predicting that Tyrion will murder her, which is why she hates him and is trying to get him killed. It also why she thinks he is responsible for the death of Joffrey. The truth is probably that the prophecy wasn't referring to Tyrion at all, and that it will be Jaime that kills her.