Throughout history people have always sought for idols, someone to look up to, someone to adore. Some people admired tyrants (which was usually problematic as you can't know who really admired them and who was forced to), some admired glorious warriors/archers/knights and some admired Gladiators.
Obviously, today we live in different times. Tyrants are less abundant, warriors, as in soldiers, do get some fame from time to time (as Chris Kyle got thanks to the movie “American Sniper”), but then again, that's pretty rare, and as for politicians, usually they are not exactly "Idol Material", so.... We idolize sports players!

Sport players are often named "The Gladiators of the 20th/21st Century". That's because just like the Gladiators, sport players make thousands of people gather around in stadiums, cheering, shouting and consuming some entertainment, all of that, thanks to them.
Obviously this tells us why sport players are popular, but does not answer your question. Well, one of the major reasons we idolize sports players is the fact that they do what they (and we) love for living! They get to play your favorite sports, do it remarkably well, and get paid for it (like really well paid). Moreover, they are usually good looking, surrounded by pretty girls and very confident, all of which are considered desired characteristics among us, humans. If we want to look into it biologically, the reason we idolize sport players is because we find them better gene carriers than us, and in one level or another we want to be like them, knowing it is not possible, we settle with idolizing them.