An outpost ship is a specialized ship that allows the creation of new bases. Move the ship over the planet you want to colonize and hit the build base button and you will create a new base, provided you have the credits to build said base.
How to counter: Since you probably won't be encountering these in massive fleets, just about anything could take them out.
Alternate purpose: Some players add a single outpost ship to a fleet to slow it down. This can slow a fleet of frigates or cruisers to speed 3, the same as HCs, Battleships and Fleet Carriers. The tactic is used to ensure that the faster ships do not overtake a previously launched slower fleet. It might also allow you to ensure that the fleet lands while you are going to be on the line.