A division in sport consists of a group of teams who compete against one another for a divisional title , or other honour.
Divisions are often organised in such a way that teams or players in any given division are comparably adept at their chosen sport, such that matches are exciting . Often this is achieved by ensuring that the victors of one division are promoted to some 'higher' division upon achieving their divisional title, swapping places with the bottom-placed team in that higher league. Variations on this idea exist in the form of playoffs. Sometimes divisions are based on geography--for instance, Major League Baseball's National League has East, West, and Central divisions. In some sports, the geographical divisions bear a very loose relation to actual geography; this is sometimes a source of controversy, as in the National Football League.
A league is such a set of divisions (or can describe an individual division within a league) in which teams can move between differently ranked divisions.
In soccer, each nation has its own football league.