In brief words, the leagues were two series of 10 scenarios each, only available online (a spanish league was also created by Edge Entertainment, which I translated to english and posted at boardgamegeek, if you are interested). Each scenario is basically a set of new rules that instruct the players to use certain elements of the game in particular conditions. For instance, each scenario requires a specific Ancient One, tells you which expansions to use (if any), which cards to remove (league 1) or gives you a narrow list of investigators to choose from (league 2). In a sense, they shape the rules of the game (adding new ones and changing them along the way) to create a sense of self-cointained mini-adventures. Naturally, each scenario is harder than the one before, and in the second league there were even a number of them that confronted the investigators with 2 ancient ones at the same time. I strongly recommend giving them a try, specially when and if the game turns a little too familiar or easy after many plays.