I have heard the name Warren Buffett. Not sure where. I have not heard of his quote though so I cannot explain the whole thing to you.
But, when someone talks about having two sides of themselves, that can mean a variety of different things.
Like your good conscience and bad conscience. For example when you have a decision to make you have one thought that you should do something bad, while the other thought is you should do something good. That is your conscience talking.
Another aspect this can refer to is mood swings. If you are in a good mood you will be happy, if you are in a bad mood you will be grumpy, and the innocent bystander had better watch out.
It could also refer to a split personality. But I doubt it.
Hope these explanations help.