Astronomers used trigonometry to calculate the distance to stars long before the term parsec was coined, but the new unit made it easier to conceptualise unfathomable distances.
A parsec is the distance from the sun to an astronomical object which has a parallax angle of one arcsecond (1/3600 of a degree). The parallax angle is found by measuring the parallax motion (or apparent movement of a star relative to stable, more distant stars) when the star is observed from opposite sides of the Sun (an interval of six months on Earth). The parallax angle is obtained by halving the angular difference in measurements.
Once the parallax angle is established you can calculate the distance to a star using trigonometry, because we know Earth’s distance from the Sun. The distance from the Sun of a body with a parallax angle of 1 arcsecond was thus defined as a unit and, thanks to Turner, named the parsec.
With the parsec defined, deriving and describing huge distances became easy, since a distance in parsecs can be calculated as the reciprocal of the parallax angle in arcseconds (if the parallax angle is 1 arcsecond, the object is 1 pc from the sun. 0.5 arcseconds means the object is 2 pc distant).
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.