A league is a group of teams that compete against each other on a regular basis. Leagues can be as small as two teams (see the former East German Oberliga) or as big as a couple dozens (National Hockey League). They can also be amateur, semi-professional or fully professional.
In European systems, it is not rare for leagues to swap one or a couple of teams at the end of each season, as per the promotion and relegation system that is common there. In North America, such a pyramidal system is very rare; leagues are however often tied to each other to various levels, as the higher ranked ones often use the lower ones as development leagues for their younger players.