"Ugatz" is spelled correctly in the Neapolitan dialect of Italian, "o cazzo." The Italian equivalent is "il cazzo." The masculine definite article "il" in Italian is "o" in Neapolitan, meaning "the."
It literally translates to "cock/penis", but is also used in Italian as the English words "fuck" or "shit."
Ugatz is derived from the Italian "u casso", literally translated as "this penis". The accompanying gesture involves dramatically lowering both hands, palms flat and facing outward, toward one's crotch. The term is used to signify a challenge to another in a variety of scenarios (see example below).
I'll never go to jail -- the DA doesn't have "ugatz" on me that will stand up in court.