Ale is an alcoholic beverage, sometimes bottled, and presumably similar to Earth ale, a form of beer.
Both Greenbean and Giles pilfers a quantity of ale—as well as some ambrosa—from the Officer's Mess for Apollo's sendoff party before Apollo's marriage to Serina. Security notices its absence and investigates the party, but is ultimately sent away by Colonel Tigh, who covers for them (TOS: "Lost Planet of the Gods, Part I").