Iam was an energy creature. It existed in a stable mini-universe made of negative energy in the Time Vortex. The Rani encountered it after being ejected from the Master's TARDIS. (TV: The Mark of the Rani) She taught it how to tunnel into normal space, and discovered it could replicate almost anything. She hoped it could copy her TARDIS' console, but it copied the Sixth Doctor's instead. Neither the Rani nor the creature realised how powerful it was, and it duplicated a large area of where the Doctor's TARDIS was travelling: 1st century BC Europe and Asia.
The duplicate console wound up in Rome, and was the source of great technological innovations for the alternate Roman Empire. The Rani never named the creature, but when the Doctor met it, he named it "Iam", from the Book of Exodus in the Bible. The Doctor convinced Iam to duplicate the entire Earth, put it in an uninhabited solar system, and transfer all the inhabitants of his initial effort there. With Iam no longer in her power and her plans routed, the Rani fled in her TARDIS. (PROSE: State of Change)