There are relic resources and mining resources that require star bases.
The relic resources give bonuses to every planets and they are very powerful (if they are working). The economic (green), manufacturing (orange), research (dark blue) work for sure and can give you up to 60% boost withe each resource fully developed. Opinions vary on whether or not the others are working right, or at all. The others are influence/culture (light blue), approval (yellow). I may be leaving one off.
The mining resources are all connected to military advantages and the whole system is still in development. They give you things like better shields, more accurate weapons etc. When this system is fully developed it will be critical to the strategic element of the game. Currently it can be used to your advantage but it is not yet a critical element
Anyway that's a quick and dirty answer