“She dreamt she sat the Iron Throne, high above them all.”

This quote details Cersei’s dream the night her father is murdered. This turns out to be prophetic, as she ends up taking over as de facto ruler of Westeros. It also shows her deeper motivation for wanting the throne and to be seen as distinct from—and superior to—everybody else.

“A Hand without a hand?”

This quote is Jaime’s response when Cersei offers him the position of Tommen’s Hand—though effectively her Hand. Jaime turns the offer down. His insecurity about his physical loss reflects a deeper psychological insecurity and a fear that he does not have the strength to help Cersei rule.

“He will need me to teach him how to rule and keep him safe from his enemies.”

Cersei is concerned about Tommen. Unlike her other son, the now dead Joffrey, Tommen is weak and sensitive, as shown by his crying at Tywin’s funeral. Cersei endeavors to change this and uses it as a justification for her effectively ruling by herself.