The Eradicator was a program that was part of a secret protocol created by General Zod on Krypton. His original duty, along with the Eradicators, was to stop Zod's enemies by any means necessary. By Zod's command, the Eradicator would send these Kryptonian's life force to a Phantom Zone projector and place their bodies in cryo-chambers.
The destruction of Krypton gave the Eradicator a humanoid but non-mechanical form, but it also robbed it of its protocol. The escape of Kal-El, however, gave the Eradicator reason to follow and when it finally arrived on Earth 0, found Jonathan Samuel Kent to have Kryptonian DNA.