Pressing the Build button will open the Planetary Structures Building screen. From here, you may build structures on the planet, such as mineral mines, factories, and defense posts. The maximum number of each that can be constructed on a planet is dependent on the colonist population. More information on how to actually build these structures can be found here.
The cost of each structure is as follows:
Structure Supplies MegaCredits Mineral Mine 1 KT 4 Factory 1 KT 3 Defense Post 1 KT 10
Mineral mines extract minerals from the planet. Each factory produces 1 KT of supplies each turn. Defense posts help protect a planet from attacking enemy ships and ground troops.
When there are not enough colonists on the planet to maintain structures on the planets surface the structures will decay at a rate of 3 structures per turn.
Additional details can be found here.