Cersei Lannister was the eldest child of Tywin and Joanna Lannister by mere moments, and the twin sister of Jaime Lannister. After Robert's Rebellion she married the new king, Robert Baratheon, and became Queen of the Seven Kingdoms.
Cersei's children are the result of an incestuous relationship with her brother, Jaime Lannister. They are thought to be Robert Baratheon's children, but this is called into question by many, including Eddard Stark, Jon Arryn and Stannis Baratheon. After King Robert's death she acts as Queen Regent for her son, Joffery Baratheon but she fails to control him during his rule.
When the capital is besieged by Renly Baratheon in the Siege of King's Landing, Cersei and her family are killed, including her son Joffery, and her father Tywin Lannister. Her other children are exiled to Essos alongside her brother, Tyrion Lannister.