From the Galactic Civilizations Wiki

[edit] Resources

Resources are rare space phenomena that provide bonuses in 1 of 5 categories:

	Morale	These resources contain a special type of fluid that increases the health of any living thing. Mining this resource will give your people a morale boost an you will receive a higher approval rating as a result.
	Economic	These resources contain a type of metal that is extremely valuable in trade. Mining this will increase your economic ability.
	Military	These resources contain a special type of energy that magnify your weapons and shielding on your ships which makes them stronger and more powerful. Your weapons and shields get a +X% bonus.
	Influence	These resources can increase your empire's influence. Mining these will be important to any civilization that is hoping to convince other civilizations to defect to them peacefully.
	Research	These resources are a type of crystal useful for vastly increasing the effectiveness of your existing research computers. They provide a bonus to empire research.

You can mine a resource by constructing a mining starbase with a constructor.