No, it's not fictional sporting events in a Fantasy work (though if you were looking for something like that, try Blood Bowl). Rather, it's a catch-all term to encompass the various games where (real world) players take control of imaginary sports teams, choose the players of their teams, and compete with other people.
So what separates this from a Sports Simulation Game like Football Manager? It's the fact that the stats and the simulation are actually taken from the actual performance of the sports it's based on. Whatever's happening in the Real Life sporting event would also affect the leagues and the teams in these Fantasy Sports. So the players would really have to pay attention to the leagues themselves. Like the actual leagues, the fantasy leagues are ubiquitous (Any sport worth its salt would have at least one) and has its own season which coincides with the actual leagues.
While there are Fantasy leagues for almost every single sport, the most notable and the most played is Fantasy Football, which flourishes in the United States. While their origins reach back before the Internet, so many (if not all) of the leagues are now played online that most Fantasy Sports could now considered Web Games.