To prefer means to like something better than something else, or to choose one thing over another when you have options. When you prefer chocolate ice cream to vanilla, chocolate is your favorite between those two choices. When your teacher prefers that students raise their hands before speaking, she's saying that's the way she'd like things done.

The word often appears with “to” or “over”: you might prefer reading to watching television, or prefer soccer over basketball. Sometimes people say they'd prefer something as a gentler way of making a request: “I'd prefer if you didn't slam the door” sounds more polite than “Don't slam the door.”

A preference is the thing you like better, or the act of choosing it. If given the choice, your preference might be pepperoni pizza. Notice that preferring something doesn't mean you hate the alternative. You can prefer warm weather while still enjoying a snowy winter day, or prefer one friend's company without disliking other friends. Preference is about ranking choices, not rejecting everything except your top pick.