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.
Enzo recognizes Kat on Galactica and calls her by her real name, "Sasha". Starbuck witnesses the altercation and confronts him later. Prior to Kat's final mission, after she has already received a lethal dose of radiation, Enzo and Kat have one final moment together (The Passage).