What does “making a league” mean?

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.

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:

An itinerary measure of distance, varying in different countries, but usually estimated roughly at about 3 miles; apparently never in regular use in England, but often occurring in poetical or rhetorical statements of distance. marine league n. a unit of distance = 3 nautical miles or 3041 fathoms. Although the league appears never to have been an English measure, leuca occurs somewhat frequently in Anglo-Latin law-books (Bracton, Fleta, etc.); it is disputed whether in these works it means one mile or two.

▸a1387 J. Trevisa tr. R. Higden Polychron. (St. John's Cambr.) (1874) V. 245 Þanne þey come to giders in þe feeldes Cathalmytes, þat conteyneþ an hondred leges [v.rr. leuges, leghes, 1432–50 lewkes] in lengþe and seventy in brede.

1398 J. Trevisa tr. Bartholomew de Glanville De Proprietatibus Rerum (1495) xv. xxii. 497 The walles of Babylone were acountyd for two lewges and an halfe.

c1400 Mandeville's Trav. (Roxb.) viii. 28 Þis ile es cccl. leeges aboute.

1474 Caxton tr. Game & Playe of Chesse (1883) iv. i. 158 After the maner of lombardye they be callid myles, and in france leukes, and in englong they be callid mylis also.

1483 Caxton tr. J. de Voragine Golden Legende 223/2 Mount Joye..is but half a leeke fro seynt James.

c1503 R. Arnold Chron. f. lxvi/1 xvi furlong make a frensh leuge [printed lenge].

a1513 R. Fabyan New Cronycles Eng. & Fraunce (1516) I. lxxxv. f. xxxiii An Hundreth Legis..wherof euery Lege conteyneth .iii. Englysshe myles.

c1515 Ld. Berners tr. Bk. Duke Huon of Burdeux (1882–7) lxxxvii. 275 A stronge castell with in a .iii. legges of Burdeux.

1528 D. Lindsay Dreme 642–4 The quantytie of the erth Circuleir Is fyftie thousand liggis..Deuidyng, aye, ane lig in mylis two.

1555 R. Eden tr. Peter Martyr of Angleria Decades of Newe Worlde i. i. f. 1v Such as are expert sea men, affyrme that euery league conteyneth foure myles.

1559 W. Cuningham Cosmogr. Glasse 57 The Gretians [measure] by furlonges: the Spaniardes, and French men by leques.

1594 T. Blundeville Exercises iii. ii. vi. f. 181v The French league containeth two of our miles, the Spanish league three, and the common league of Germany foure, and the great league of Germanie containeth fiue of our miles.

a1616 Shakespeare Tempest (1623) i. ii. 145 They hurried vs a-boord a Barke, Bore vs some Leagues to Sea.

1774 O. Goldsmith Hist. Earth I. 42 At Touraine, in France..there is a plain of about nine leagues long, and as many broad.

a1824 Byron Childe Harold iv. in Wks. (1837) 48/1 I never yet saw the picture..which came a league within my conception.

1828 J. M. Spearman Brit. Gunner 268 A league at sea..contains 3000 geometrical paces, or 3 English miles.

1843 G. Borrow Bible in Spain ii. xii.251 The village of Finisterra was distant about a league and a half.

1845 R. Ford Hand-bk. Travellers in Spain I. i. 15 The Spanish league is somewhat less than three miles and a half English.

1855 Tennyson Charge Light Brigade i, in Maud & Other Poems 151
Half a league, half a league, Half a league onward.

1878 R. Browning La Saisiaz 25 Can I..sharpen ear to recognize Sound o'er league and league of silence?