When a skirt is cut at an angle, with one side higher than the other, it has a bias cut. Being biased is kind of lopsided too: a biased person favors one side or issue over another.
While biased can just mean having a preference for one thing over another, it also is synonymous with "prejudiced," and that prejudice can be taken to the extreme. Sometimes a person is so biased, or is leaning so far in one direction, that it's hard to see the other position, creating unfairness in an argument or decision. Often, though, it's used more lightly: "My mom makes the best brownies in the world, but I might be a little biased."