Corruption is measured on a scale of 0 to 100, starts at 0, increases upon doing certain things (mainly having sex with demonic or heavily corrupted NPCs, and doing morally bad things), and decreases upon doing certain other things (mainly doing morally good things, though there's also a dedicated cleansing/meditation thingy that lowers it a lot faster than other methods).
Upon reaching 75 Corruption, your personality changes to Dark Knight, which causes you to act more aggressively and/or anti-heroic depending on the author; dropping below 25 Corruption will switch your personality back to the default Champion. The Bimbo personality overrides both.
Certain items can only be equipped if your Corruption is above or below a certain threshold - the Dawnsword's variants are two such items, and which version you get matches your personality if and when you obtain it.
Some options are only available if your Corruption is high or low enough, and being at 100 Corruption puts you at risk of certain Bad Ends where you lose your soul (or its simulacrum, if you're soulbound).