General Zod, Ursa, and Non are the three arch-criminals condemned by Jor-El to a prison called the Phantom Zone at the beginning of Superman: The Movie (before Krypton was destroyed).
The Phantom Zone travels through space for many years, and happens to pass near Earth at the same time that Superman throws a live nuclear bomb deep into space. The explosion destroys the Phantom Zone, freeing the arch-criminals--who, due to their proximity to the Earth and our Sun, find themselves endowed with the same powers that Superman has.
Meanwhile, Lois Lane, Superman's love interest and fellow reporter at the Daily Planet with Superman's alter-ego, Clark Kent, has discovered Superman's secret identity and professes her love for him. Superman feels the same for Lois, and so they fly off together to his Fortress of Solitude, far to the north and away from any civilization.
While Superman is away, the three Kryptonian super-villains arrive on Earth and wreak all sorts of havoc, quickly taking over the entire world. They meet up with Lex Luthor, who reveals to them Superman's existence and notes that he is Kal-El, the son of their jailer. Meanwhile, Superman has given up his powers in order to be "mortal" and so be with the woman he loves--when the couple return to civilization, they learn what has happened and so Clark makes the journey back to the north in an attempt to regain his powers so as to do battle with the super-villains.
Clark does regain his powers and is again Superman, setting the stage for a climactic battle in the city of Metropolis as the three super-villains attempt to take their revenge on the son of their jailer, while Superman has to figure out how to end this super-threat to the Earth once and for all.