means A group of teams, people, or states bound together for a common purpose — or, in older usage, a rough measure of distance, traditionally about three miles.

from Two separate words wearing one coat. The distance 'league' comes through Old French 'lieue' from Late Latin 'leuga' or 'leuca' — a Gaulish measure the Romans borrowed, said to be the distance an ordinary person could walk in an hour, which is exactly why nobody agreed on it. The alliance 'league' arrived later, in the 15th century, from Old French 'ligue' via Italian 'liga,' from Latin 'ligare,' to bind or tie — the same root that gives us 'ligament' and 'oblige.' So one league measures how far apart you are; the other measures who you're tied to.