Esdeath is a high-ranking general of the Empire, and leader of the Jaegers. She enjoys torturing her enemies slowly, seen when she used her Teigu to put large blocks of ice in a cauldron so that the people inside would die slower and suffer more. Despite her sadistic actions, she is actually shown to have a compassionate heart when it comes to the lives of her men and others close to her.
Her name in japanese, Esdesu, is a pun meaning "I am S" to show how sadistic she is.
(Source: Akame ga Kill! Wikia)