The phrase Roman holiday denotes an occasion on which enjoyment or profit is derived from the suffering or discomfiture of others.

This phrase originated in the following passage (which refers the violent gladiatorial spectacles held by the ancient Romans on holidays) from Childe Harold’s Pilgrimage. Canto the Fourth (London: John Murray, 1818), by the English poet George Gordon Byron (1788-1824):

I see before me the Gladiator lie:
He leans upon his hand—his manly brow
Consents to death, but conquers agony,
And his drooped head sinks gradually low—
And through his side the last drops, ebbing slow
From the red gash, fall heavy, one by one,
Like the first of a thunder-shower; […]
[…]
He reck’d not of the life he lost nor prize,
But where his rude hut by the Danube lay
There were his young barbarians all at play,
There was their Dacian mother—he, their sire,
Butcher’d to make a Roman holiday.

The following explanations are from Green-Eyed Monsters & Good Samaritans: Literary Allusions in Everyday Language (New York: McGraw-Hill, 2006), by Leonard Mann:

On September 3, 1925, the USS Shenandoah, a helium-filled airship, plunged from the air into a farm field in Noble County, Ohio, and in that crash thirteen airmen died. Almost immediately a great many of the curious, the callous, and the greedy descended upon that scene. Hawkers sold food and drink, scavengers stripped fabric from the ruined ship and sold pieces as souvenirs, nearby landowners rented parking spaces, and a general carnival atmosphere prevailed. Altogether, it was a shameful reaction to human tragedy, a classic instance of a Roman holiday, that is, a vulture’s feeding frenzy in which a group of people, for their own pleasure, take advantage of the sufferings or misfortunes of others.
Why is such known as a Roman holiday? Because of something written a couple of centuries ago by George Gordon Byron. The story actually begins about 320 B.C. when a Greek artist sculpted the statue of a dying man, a strong man in the prime of life but with a mortal wound in his side, the sort of wound a spear would make. Centuries later, an Italian sculptor found the statue and made a copy of it.
That being the time of the Gallic Wars, the statue was named The Dying Gaul. It represented a prisoner taken by the Romans in the wars and then forced to fight in their arenas for the amusement of their nobles, there wounded to the point of death and now dying. The statue was placed in the Capitoline Museum in Rome, and there in 1817 or 1818 it was viewed by Byron, who was at the time writing Childe Harold’s Pilgrimage. The poet wrote of the man he saw in the statue: he wrote of the man’s dying vision of his home by the distant Danube and of how he is now dying, “butcher’d to make a Roman holiday” (canto iv, line 1267).

The first two occurrences of the phrase Roman holiday that I have found are quotations from Byron’s poem, and refer to gladiatorial combat in ancient Rome:

1-: From Italy (London: Henry Colburn and Co., 1821), by the Irish author Sydney Morgan (née Owenson – c.1776-1859):

This is the Coliseum—the last and noblest monument of Roman grandeur, and Roman crime—erected by the sweat and labour of millions of captives, for the purpose of giving the last touch of degradation to a people, whose flagging spirit policy sought to replace by brutal ferocity. The first day’s games given in this sumptuous butchery cost the nation eleven millions of gold. The blood of five thousand animals bathed its arena. Man and his natural enemy the beast of the desert, the conqueror and conquered, writhed in agony together on its ensanguined floor; and eighty-seven thousand spectators raised their horrid plaudits, while captive warriors were slain
                                        “To make a Roman holiday.”

2-: From Solitary Walks through many Lands (London: Hurst, Chance, and Co., 1828), by Derwent Conway, pen name of the Scottish travel writer Henry David Inglis (1795-1835):

With respect to the architectural remains which are to be found in Italy,—every one knows, that the Romans executed only, but did not invent. Those remains are indeed interesting; but the interest arises from their inherent beauty, and would exist, although the building once upheld by the columns that lie prostrate, had never been used as baths by Vespasian, nor resounded with the shouts of a brutal multitude, at the butcheries of “a Roman holiday.”

The first two transferred uses of the phrase Roman holiday that I have found are as follows:

1-: From the review of Harlequin and Georgey Barnewell; or, the London Prentice, a pantomime produced at Covent Garden, London—review published in The True Sun (London, England) of Tuesday 27^th December 1836:

The last transformation was one of the best. A Richmond omnibus is turned into Green’s flying omnibus balloon, just ready to start from Vauxhall-gardens for America. The Duke of Brunswick enters just at the moment of ascent. He enters, and out he tumbles, umbrella and all. This excited much laughter. Madame Louise Irvine ascended from the stage to the gallery on the tight rope, with great nerve and resolution. Such exhibitions should not only be discouraged by the public, but be prevented by those in authority. The audience last night repeatedly exhibited strong marks of disapprobation. Some day or other a life will be lost in these terrific ascents, and when some one is “butchered to make a Roman holiday,” the attempt will be discontinued for the future. Why not at once?

2-: From the account of a parliamentary election in Chester, published in The Chester Chronicle, and Cheshire and North Wales Advertiser (Chester, Cheshire, England) of Friday 28^th July 1837:

A more miserable display and a more ignominious defeat never followed each other in the annals of tory electioneering. The whole attempt was a farce, and their candidate a victim selected for the sport and gibes of the people, was metaphorically “butchered to make a Roman holiday.”