Ser Jaime Lannister is the eldest son of Tywin, younger twin brother of Cersei, and older brother of Tyrion Lannister. He is involved in an incestuous relationship with Cersei, and unknown to most, the biological father of her three children, Joffrey, Myrcella, and Tommen.
Jaime previously served in the Kingsguard of Aerys Targaryen, known as the Mad King, before infamously backstabbing him during the Sack of King's Landing, earning Jaime the nickname of the Kingslayer. He continued to serve in the Kingsguard of Robert Baratheon, and as Lord Commander for Robert's alleged sons Joffrey and Tommen. However, a confrontation with the Faith of the Seven led to his dismissal from the sworn order.
With Cersei's ascension to the Iron Throne and in light of the death of their uncle, Ser Kevan Lannister, Jaime was appointed as the new commander of the Lannister armies.
(Source GOT wiki)