This assignment will tell your spies to steal buildings and plans. Of course, it would be very difficult to pick up a building and stuff it in his trench coat, so what he's really doing is stealing the plans for the building. When your spy is successful, plans will be added to his home planet. You can view your plans in your build list or on a building when you go to upgrade it, or in your Planetary Command Center.
When stealing a plan that the planet already has, nothing really happens to that planet other than they no longer have the plan. However, if you steal a building, what it's really doing is turning one level of their building into a plan. So in effect, you are downgrading their building to produce a plan. Obviously this can be quite devastating, therefore you can only run appropriate technology on a non-capitol planet that is owned by an empire no lower than 100 ranks below you in the empire stats.
This mission is unavailable if you are on a planet that is in your alliance.