To be blunt, When you gain ego and if you have a cock, then your cock gets bigger. If you drink a ego potion and you don't have a cock, you get one. You can get more ego by picking more aggressive options before starting a battle and winning.
As others have said, it affects your manhood. But in addition to gaining more ego for being agressive, you also gain more ego for defeating larger foes. In particular, The Beast seems to give substantial amounts of ego once he grows a few times. It gets kinda ridiculous.
