Nautical miles measure distance. 1 nautical mile is the angular distance of 1 minute of arc on the earth's surface. As these differ slightly (6108' at pole c.f. 6046' at equator) 6080 was adopted (this being it's approximate value in the English Channel). The International nautical mile is 1852 metres, so is very slightly different from the UK nautical mile.
A nautical league was 6,080 yards - or three nautical miles (each league being 6,080 feet). Note that there also US Leagues, UK Leagues and UK Nautical Leagues which all differ.