Generally speaking, you increase your corruption level by willingly making lewd, one-off choices during scenes, or letting yourself get grabbed and 'affected' by enemies such as the slime-dragon's slimesuiting.
Right now, that last thing I mentioned is a way that you can increase corruption infinitely (though it's a bit of a slow method).
Corruption right now changes the dreams you witness when you rest, it unlocks certain lewd scenes, and it can make certain lewd decisions automatically instead of offering you the chance to avoid them.