There are two answer generally given: rising nationalist sentiment amongst the general public in response to political currents in the period 1914-1918, combined with the enlargement of the franchise following the Fourth Reform Act 1918. I will start with the latter, as it is mere fact.

In the 1910 election, the Irish Parliamentary Party received 90,000 votes, securing 43.6% of the vote. In 1918, they received more than 200,000 votes. Sinn Féin received almost 500,000 votes, which translated to just shy of 47% of the vote on the island. The Irish electorate, after the implementation of the Representation of the People Act 1918 (Fourth Reform Act), grew, as occurred across the UK, by almost 300%. This is owing to the radical expansion of franchise - very suddenly, all men over 21 and most women over 30 (their franchise was tied to owning, or being married to a man who owned, £5 or greater worth of property) were allowed to vote. The traditional constituency of the Irish Parliamentary Party was a relatively wealthy, and older, middle class. The IPPs vote swelled, but most voted for Sinn Féin. Why? That's the tricky part, and the influence of each factor is contested. Many who write on this period tend to be Irish, and historians interested in nationalist history tend to have a bias. That's unavoidable, though the sources I've listed at the end come from historians who tend to be amongst the least controversial. I have done my best to limit my own personal biases.

The IPP had, finally, successfully secured a timeline for the implementation of Home Rule in 1914. However, the outbreak of the Great War postponed this for a minimum of twelve months. It was never implemented. When the 1918 election came along, the strategy of the IPP had seemingly failed and there was a risk of conflict breaking out in Ireland to stall the implementation of Home Rule after the War. This was threated by loyalist paramilitaries in the north of Ireland, in particular the Ulster Volunteers.

With Home Rule not seeming likely, many Irish felt that only a party which could act decisively would represent their interest. Sinn Féin, swelled with activists and veterans of the 1916 Rising and the internment camps, promised to establish an Irish Republic if they won the 1918 election.

But why did the people support such a radical programme in 1918? Had they not been against the Rising? This is popularly held to be true - the Rising was greeted with antipathy at best, if not hostility, initially. Many Irishmen were fighting abroad and it was seen as a betrayal of those valiant men fighting overseas. The Irish Volunteers explicitly went abroad to display their loyalty to the Crown, in hopes of securing Home Rule. However, when the leaders of the Rising were summarily executed in 1916, the British in Ireland proved their point for them - there never would be equal treatment of the Irish by the British, as displayed by the lack of empathy when James Connolly was shot in a chair, as he was injured and could not stand.

Further, and perhaps more importantly (the above is a core component of Irish republican mythology, and thus often overstated) there was a fear of conscription in 1918. The Irish had volunteered to fight, but many felt that the war in Europe was not their war. With Home Rule postponed indefinitely and conscription seemingly looming (though there was never a real chance of it happening), many Irish felt that the British did not seek to treat them as equals. They were denied political rights which had been promised, which convinced many to vote for the nationalist/republican party.

There is also the socio-economic factor - Ireland was poor, relative to England, and there was a long fostered resentment of this. Throughout the 19th Century, the land reform movement was very successful in returning land from absentee landlords to the Irish people but resentment for economic exploitation remained. The Great Famine had occurred in the mid-1800s, and was not forgotten. Many of those who were recently enfranchised by the Reform Act harboured resentment towards the British state, though had never been inclined to fight the British army. The election of 1918 and Sinn Féin's platform advocating independence gave those of an exploited socio-economic class a democratic say - and they voted for independence.

Seemingly, the successful prevention of conscription was associated, wrongly, with Sinn Féin. Sinn Féin was also, wrongly initially, until the takeover at the 1917 party conference, associated with the Rising. They had the sympathy of the public, and represented a change to the failed politics of the IPP. The leadership of the IPP, such as John Dillon and Redmond before him, appeared aloof compared to the young, vigorous and militant leadership of Sinn Féin - Eamonn De Valera, Michael Collins, etc.

Did Home Rule become unacceptable? No. It was certainly acceptable. However, it was believed that it would never come, especially in the face of violence which would come from northern unionists. Following the harsh treatment of the Rising leadership and the conscription crisis, nationalist sentiment amongst the lower class in Ireland rose, stoked by Sinn Féin. Sinn Féin promised an immediate solution, and after their sweeping victory in Ireland in 1918, entirely facilitated by the expansion of franchise as most of those who voted for Sinn Féin had never been allowed vote before, they proclaimed, as promised, an independent Ireland.

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Here is a list of some good resources for reading about Home Rule, Nationalism, and the rise of Sinn Féin in this period.

Jackson, A., Home Rule: An Irish History, 1800–2000 (London, 2003)

Garvin, T., The evolution of Irish nationalist politics

Boyce, D. G., Nationalism in Ireland (1982)

O'Day, A., Irish Home Rule, 1867–1921 (1998)

Laffan, M., The resurrection of Ireland: the Sinn Féin party, 1916–1923 (1999)

If I may point out u/Jaehaerys_Rex has left out some significant facts that ultimately led to the 1916 Rising and the War of Independence. Also, to describe the Rising as unpopular is to misread some of the reasons behind this. The sentiments and aspirations expressed by the leadership of 1916 were not unpopular – the issues concerning the Rising had much to do with the perception of success that the Rising could bring about. This was especially seen in the person of Eóin MacNeill, himself an organiser of the Irish Volunteers, who said the Rising was doomed to failure and he couldn’t therefore support it. Some eyewitness accounts also tell of growing public support as the week of the Rising continued [and prior to the execution of the leaders] - reports of admiration that such a small grump, just over 1,000 men and women, could hold out so long against overwhelming odds of a British army of around 28,000.

The IPP had, finally, successfully secured a timeline for the implementation of Home Rule in 1914.

There was a major problem with this however. The Home Rule bill by 1914 had a partition clause inserted into it. This was not resolved at the Buckingham Palace conference in July 1914. This was an anathema to Irish nationalists who expressed concerns that the IPP leadership - in the person of John Redmond - seemed willing to let this happen. We know this from source material of the time that Redmond openly expressed in letters that partition was not an issue for them. That a large part of Ulster would not be part of a Home Rule united Ireland bill caused ripples within the nationalist movement. There was also the issue of what the Home Rule bill had become. It had become so watered down that Home Rule was by now little more than local government under the complete control of Westminster.

Pre WWI there was evidence of violent resistance to Home Rule in the Ulster region as paramilitary units formed, encouraged by support from the English Conservative Party, and ultimately by the British army. The Ulster Volunteer Force [UVF] was formed in 1912 and when they imported arms the British army refused orders to disarm them. In response to this threat the Irish Volunteers were formed in 1913 [by Eóin MacNeill and Bulmer Hobson] with the pledge to fight the UVF and the British in order to establish Home Rule under a united Ireland. They numbered around 200,000. Not an insignificant number.

By the summer of 1914 the country was on the brink of civil war when WWI broke out. Redmond directed the Irish Volunteers to support the war effort in order to secure Home Rule. He made no mention of his support for partition in his speech. The Irish Volunteers split on the issue of the war with the majority going to war with the intention of securing Home Rule.

When the 1916 Rising was planned it was done with the intention of establishing a united Ireland, a republic. In spite of the failure, and the knowledge that the Rising would fail, Pearse had read the growing mood in Ireland very well. [The public response to the 1913 Bachelors Walk massacre had demonstrated how riled up the Irish public was against British aggression]. This sentiment was carried over by Sinn Féin – who had no part in the Rising - into the 1918 election when they won 73 out of a total of 103 seats and declared Irish independence and seceded from the United Kingdom.

It [Home Rule] was never implemented.

Yes it was actually. The Home Rule bill was passed by the Westminster Parliament in 1920. Partition had become enshrined in it by then and six of the Ulster counties were given a Home Rule government in Belfast. Dublin was also given a Home Rule parliament but this was not recognised by the Dublin Sinn Féiners who had set up an independent government which they named Dáil Éireann in Jan 1919. The Irish War of Independence was in full swing by now. At the Treaty in Dec 1921 the Home Rule bill for Dublin was abolished and the Irish Free State was established. The Irish Free State was recognised by the British as a withdrawal from the United Kingdom.

Edit: typos and adding content