rum-runner n.

"liquor distilled from the juice of sugar cane or molasses," 1650s, apparently a shortening of rumbullion (1651), rombostion (1652), words all of uncertain origin, but suspicion falls on rum (adj.) "excellent, fine, good, valuable;" the phrase rum bouse "good liquor" is attested from 1560s and through 17c. The English word was borrowed into Dutch, German, Swedish, Danish, Spanish, Portuguese, Italian, French, and Russian.

In the Library of Trinity College, Dublin, is a manuscript entitled "A briefe description of the Island of Barbados." It is undated but from internal evidence it must have been written about the year 1651. In describing the various drinks in vogue in Barbados, the writer says : "The chief fudling they make in the Island is Rumbullion alias Kill-Divill, and this is made of sugar canes distilled, a hot, hellish, and terrible liquor. ["The Etymology of the Word Rum,"  in Timehri, 1885]

Rum was used from c.1800 in North America as a general (hostile) name for intoxicating liquors, hence rum-runner and much other Prohibition-era slang.

Rum I take to be the name which unwashed moralists apply alike to the product distilled from molasses and the noblest juices of the vineyard. Burgundy in "all its sunset glow" is rum. Champagne, soul of "the foaming grape of Eastern France," is rum. ... Sir, I repudiate the loathsome vulgarism as an insult to the first miracle wrought by the Founder of our religion! [Oliver Wendell Holmes, "The Autocrat of the Breakfast-Table," 1871]

c. 1300, "messenger on foot," agent noun from run (v.). The meaning "one who runs, a racer" is from early 14c.

With many technical senses. The meaning "smuggler, one who risks or evades dangers, impediments, or legal restrictions" is by 1721; the sense of "police officer" is from 1771. The botanical meaning "rooting stem of a plant" is from 1660s. The sense of "embroidered cloth for a table" is from 1888. In baseball, "a base-runner," by 1845.