Allusions are brief and often indirect references to historically, culturally, or mythologically significant characters, places, or occurrences. Allusions allow authors to set the stage upon which characters act and plots occur, but they require the reader to be informed about the relevant background in order to fully grasp their significance. 

In Liam O'Flaherty's short story "The Sniper," the action occurs in Dublin during the Irish Civil War. The particular battle described in the story is set on the O'Connell Bridge and O'Connell Street.

O'Flaherty's use of this street is an allusion. O'Flaherty never elaborates on O'Connell Street's significance, but it is an important part of Dublin's geography and has a significant role in Ireland's bloody history. O'Connell Street was (and still remains) the main thoroughfare through Dublin, playing a large part in the city's economy. It was also the site of several major battles, both during the Irish Civil War and during the Easter Uprising six years earlier. Notably, in 1922, O'Connell Street was the site of a seven-day skirmish ended by point-blank artillery brought in by armored cars—a detail obliquely referenced by the armored car carrying the titular sniper's first victim.

The reference to Dublin, combined with the references to Republicans and Free Staters are all allusions; references to persons and places which are unexplained but help us to understand the nuances of the story.  These references all combine to point to the likely setting of the story: a civil war that took place in Ireland in the early 1920s between those people who believed that the whole of Ireland should be united as an independent republic, totally separate from England (these are the Republicans the narrator mentions), and those who do not support a united Ireland, completely separate from England (these are the Free Staters).  "Free Stater" is also often used as a derogatory term by those in Northern Ireland to describe those who live in the southern part of the country and can describe those individuals who left the Republican movement.  

An allusion is a brief reference to a person, place, thing or idea which is of cultural, literary, historical or political importance. In Liam O'Flaherty's short story "The Sniper" the third person narrator mentions the fighting surrounding the "Four Courts" building in Dublin. This is an allusion to governmental buildings which were highly significant in the Battle of Dublin during the Irish Civil War. The Republican army, of which the protagonist sniper was a part, briefly occupied the buildings before being eventually bombed to the point of surrender by the Free State army which had been supplied with "heavy guns" (also referred to in the story) by the British. Though never explicitly stated in the story, the sniper's task was to help protect the area around the Four Courts.