When you click a planet that you have in the menu, you can see a screen like one above.
Planet stats(At the left of the screen)
Prosperity : indicates how much your planet has been developed.
MAX LV : indicates until what level you can upgrade the buildings in the planet.
Environment (on the scressn, "Research") : indicates how much the planet boosts its research lab.
Functions(At the bottom of the screen)
Sell : Sell your planet if you don't want it anymore. Be cautious! You can't get it back permanently, and you will get only part of the price.
Place/Replace :Dispatch a hero or change the current planet minister. His/her skill or government stat affects planet performance significantly.
Inspection : Order the planet minister to inspect the planet. The minister will try to find something in the planet. The result depends on his/her stats. (without the planet minster, The function will be invail)
Buildings(In the middle of the screen) : by clicking a building, you can upgare it for more benefits.
Residential facility : Produces gold stably by a minute.(Detail)
Mining Facility : Produces mineral stably by a minute.(Detail)
Element processing Facility : Produces cosments a minute. However, what it produces is depends on how war is going. Check Resource page to learn more.(Detail)
Energy plant : Supplies Energy which determine How many ships you can have in your fleets.(Detail)
Research lab : Supplies Research which affects research costs and unlock new technologies.(Detail)
Fleet production line : Supplies Production which affects costs of ships.(Detail)