They are a spaceship computer found on an abandoned spaceship, who helps Baxter Stockman fight the Ninja Turtles and Shredder. They claim to have been lonely over the millions of years they were trapped underground, and thus is very attached to the first person they encountered. After the ship falls apart, both are defeated and left stranded in the Dimensional limbo.
The Spaceship Computer was still with Baxter Stockman in "Son of Return of the Fly II." They helped Baxter Stockman escape the Dimensional limbo and return to Earth where they helped Baxter capture the Turtles so that Baxter can fight Shredder. Upon finding a Solid Energy Generator, the Spaceship Computer had Baxter insert this device into their slot, which allowed them to grow an energy-based body and create various devices for Baxter's use.
However, Krang and Shredder had plans to steal the computer for their own ends. The Spaceship Computer was destroyed in the resulting battle when Leonardo self-destructed the Generator, leaving only a broken circuit board that still spoke to Baxter.
In an alternate retelling in "Revenge of the Fly," Baxter and the Spaceship Computer are freed from the dimensional limbo by Krang. He plugged the Spaceship Computer into the Technodrome allowing Baxter to take control of it. After Baxter created some mutant insects, the Spaceship Computer reminded him that he had forgotten about the Turtles causing Baxter to use his insect minions to capture them. The Spaceship Computer left behind in the ensuing chaos caused by the Turtles and the mutant insects. They were never seen again after this instance.