No, it's not fictional sporting events in a Fantasy work (that is a Fictional Sport). Rather, it's a catch-all term to encompass the various games where (real world) players create imaginary sports teams, choose the players of their teams, and compete with other people.
Unlike a Sports Simulation Game like Football Manager, Fantasy Sports are based on the actual performance of the players in the sports it's based on. Most begin with players drafting representations of real athletes for their teams, effectively working as a combination of a real sports draft and a card game. Points, winners and losers are solely based on the performance of the Real Life athletes that players have added to their teams. Generally this means you need pretty healthy knowledge of whichever real life league your fantasy league is based on. 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. At this point even things that are in no way sporting events have had Fantasy Leagues created, perhaps most famously The Bachelor.
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, most Fantasy Sports could now be considered Web Games, as dozens of different websites offer fantasy leagues of all sorts, and they are played almost exclusively online at this point.
Not to be confused with the 1990s British TV show Fantasy Football League, although it was based on this concept.