Corruption is an empire wide effect that makes every planet in your empire a little less productive.
Corruption is growing with the size of your empire. The more planets you have got, the higher the corruption in your empire. The higher the corruption, the more food, production points, mined ship-resources, research points and planet-income are wasted on every planet.
However, you can influence the amount of empire-wide corruption with your Reputation. A positive reputation will reduce the amount of corruption in your empire. A bad reputation on the other side will increase corruption even further!
Empire-Wide Corruption has of course a very strong impact on the corruption level on each planet.
Note that the empire-wide corruption percentage may not be the corruption that is applied at all planets. The corruption applied to each planet is a function of population count. When a planet has reached 75% of its population limit, then it will reach the maximum corruption, i.e. the percentage listed in “Empire Overview”. The corruption in a planet with less than 75% population is calculated as follows:
But that is not all, you can do something about the corruption level on each planet: you can build Propaganda Offices, and even station Military on your planets to increase population loyalty - and by that reduce the corruption level on individual planets. Read Loyalty and Corruption level of a Planet for more details.
The resulting corruption level (influenced by empire-wide corruption as well as the local planet’s population loyalty) impacts the productivity of your planet. So in order to keep productivity high as your empire grows, either keep empire-wide corruption low (by maintaining a positive reputation), and/or increase the loyalty level on individual planets.