Enzo is a former criminal that used to work with Kat prior to the Cylon attack. He was a drug supplier who provided her with drugs to run; they had also apparently been sexually intimate.
During the episode "The Passage", Enzo recognized Kat on the Galactica and called her by her real name "Sasha". Starbuck witnessed the altercation and confronted him later. Prior to Kat's final mission, after she had already received a lethal dose of radiation, Enzo and Kat had one final moment together.