They're the best in the world at whatever they do. In Major League Baseball, people wouldn't think too highly of a utility infielder, but you have to consider the fact that he is being paid a lot of money because he is one of the best infielders there is around. Greg Maddux isn't just a really good, highly paid pitcher, he's the most talented pitcher there is to currently offer. Professional athletes are a special group of people. Their superior talent has been recognized, and now they are being acknowledged for it, by way of monetary compensation.
Good athletes are in high demand.
Owners will pay very large sums of money to have a winning team. It's as simple as that. Entertain 50,000 adoring fans, win the game, and try not to scratch your new Mercedes Benz on the way out of the parking lot. And that brings me to my next point. Pro athletes compete in a game.