Like Fighter is a game where you judge everything with the Facebook "Like" button. Using socially-driven statistical algorithms, Like Fighter randomly displays two things. You choose which one you like. Then Like Fighter shows you two more.
Like Fighter is a Facebook application, so that's the actual Facebook "Like" button you're clicking on. Each time you click it, the Like button posts an item to the "Recent Activity" section of your Facebook feed, revealing your bold convictions to your friends. You can easily remove these from your feed if they offend you.
In order to further human understanding in this modern age, Like Fighter keeps statistics of how many people like different things. You can see this information here.
Like Fighter only stores your numeric id and what you've liked so it doesn't show you the same combination twice. Like Fighter does not store or share any personal information about you or your friends. Ever. For real. Like Fighter thinks that sort of thing is stupid and mean.