Terraforming Platform Ships deploy into Terraforming Platform plans when they reach a destination planet. They are used to allow a species to inhabit a planet they couldn't normally exist on.
You need a Terraforming Lab to build a Terraforming Platform Ship. The Terraforming Platform plan that you get will have a level equal to the level of your Terraforming Lab.
Purchasing Terrforming Ships without the appropriate university level will not work! You can skip the requirement of the lab using this route, but not the required university level.
The level of the platform created by the ship is determined by the level of the terraforming lab on the planet that launched the ship. For example, if you launch a terraforming platform ship from a planet without a terraforming lab, then the platform plan you get on the planet will be level 1. But if you have a level 3 lab, then the plan will be 1+3, resulting in a level 4 platform.