Real Dictionary

league
A league is a group of people, clubs, or countries that have joined together for a particular purpose, or because they share a common interest.
countable noun: A league is a group of teams that play the same sport or activity against each other.
countable noun: You use the word league to make comparisons between different people or things, especially in terms of their quality.

league in American English 1
a compact or covenant made by nations, groups, or individuals for promoting common interests, assuring mutual protection, etc.
to form into a league
noun: a covenant or compact made between persons, parties, states, etc., for the promotion or maintenance of common interests or for mutual assistance or service

league in American English 2
a unit of linear measure varying in different times and countries: in English-speaking countries it is usually about 3 statute miles or 3 nautical miles
noun: a unit of distance, varying at different periods and in different countries, in English-speaking countries usually estimated roughly at 3 miles (4.8 kilometers)

league in British English 1
noun: an association or union of persons, nations, etc, formed to promote the interests of its members
verb: to form or be formed into a league

league in British English 2
noun: an obsolete unit of distance of varying length. It is commonly equal to 3 miles