I think this is an idiom/expression referring to happiness or relief, but it might also be a sailing term used by sailors. It's from Christopher Columbus’s journal (1492), as he writes about approaching (what he thought was) India from the Atlantic Ocean.
They saw petrels and a green bulrush near the ship. The men of the caravel Pinta saw a cane and a stick, and took on board another small stick that appeared to have been worked with iron, and a piece of cane, and other vegetation originating on land, and a small plank. The men of the caravel Nina also saw other signs of land and a small stick loaded with barnacles. With these signs everyone breathed more easily and cheered up. On this day, up to sunset, they made 27 leagues.
Best Answer
A league is a unit of distance, having many definitions. In the time of Christopher Columbus, the legua or Spanish league was around three or four nautical miles.
The phrase they made 27 leagues indicates that the ship travelled 27 leagues in distance that day.
You may have heard of Jules Verne's 19th Century science fiction novel Twenty Thousand Leagues Under the Sea, which references the league in its title.
The full OED entry is as follows, with examples: