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The information below about this shanty is from Wikipedia:
The shanty was sung to accompany certain work tasks aboard sailing ships, especially those that required a bright walking pace. It is believed to originate in the early 19th century or before, during a period when ships' crews, especially those of military vessels, were large enough to permit hauling a rope whilst simply marching along the deck. With the advent of merchant packet and clipper ships and their smaller crews, which required different working methods, use of the shanty appears to have declined or shifted to other, minor tasks.
"Drunken Sailor" was revived as a popular song among non-sailors in the 20th century, and grew to become one of the best-known songs of the shanty repertoire among mainstream audiences. It has been performed and recorded by many musical artists and appeared in many popular media.
Although the song's lyrics vary, they usually contain some variant of the question, "What shall we do with a drunken sailor, early in the morning?" In some styles of performance, each successive verse suggests a method of sobering or punishing the drunken sailor. In other styles, further questions are asked and answered about different people.
The song shares its tune with the traditional Irish folk song "Óró sé do bheatha abhaile" (English: "Oh-ro welcome home"), possibly a Jacobite song, as the traditional version mentions "Séarlas Óg" ("Young Charles" in Irish), referring to Bonnie Prince Charlie and dating the song to the third Jacobite rising of 1745–6. The tune appears as number 1425 in George Petrie's The Complete Collection of Irish Music (1855) under the title Ó ro! ’sé do ḃeaṫa a ḃaile (modern script: Ó ro! ’sé do bheatha a bhaile) and is marked “Ancient clan march.” It can also be found at number 983 (also marked “Ancient Clan March”) and as a fragment at number 1056, titled Welcome home Prince Charley. "Óró sé do bheatha abhaile" was often sung by the Irish Volunteers during the Easter Rising, but with different, non-sectarian lyrics composed by Pádraig Pearse.