A prize is the reward or recognition a winner gets. When you win first prize in your state spelling bee, you might get a medal and a trip to the national competition in Washington, DC.
Many prizes are given for hard work, athletic skill, or superior intellect, but it's also possible to win a prize from sheer good luck. The prize for a winning lottery ticket, for example, might be a million dollars. If your dog comes in first at an obedience competition, you can call her your "prize pup." And if you adore and value that dog more than anything else, you can say you prize her.