Prefer means to like better. If your parents prefer your sister to you, chances are her allowance will be higher and you'll get blamed for things she's done.
If someone offers you hamburgers and hot dogs, it's more polite to say, "I'd prefer a hot dog," then "Blech, hamburgers. Gag me!" Note that prefer means not just to like, but to like better––you're comparing two or more things. Whether it be chocolate ice cream over other flavors, or getting going first thing in the morning as opposed to lounging in your PJs, what you prefer is called your preference. And if you like them all the same, you can say you have no preference