Click on the starbase and you should see a circle of effect (in the color of your race- blue default for humans.)
This is the area the base effects. Any planets, trade routes in that circle of effect benefit from the base, depending on the modules you have on the base.
For instance, you have four economy bases that have Earth in the area of effect, then Earth benefits from whatever bonuses that base has that are applicable to planets. So, if you max out the Social/Military/Research production modules on each of these bases, then Earth is getting some sweet benefits!
For one game, I was jammed in the corner. Typically this can be bad, but I found it was great when dealing with trade routes. Al of my trade routes followed the same line through about 4 sectors before they broke off to their planets. In each of these sectors I crammed 3-4 economy bases maxed on trade benefits. So Basically, 90% of the complete of all my trade routes were covered with stacking bonuses. Let's just say money was no longer an issue for QUITE some time!
Edit: keep in mind there is a 3 parsec limitation between bases (unless a base is a resource mining base.) But this is ONLY a factor in the same SECTOR. Thus, you can have econ bases right next to each other if there is a sector line beteen the two. I've had 4 econ bases right next to each other at the connection point of 4 sectors. All four covered about 6-8 planets.