G'day Kate -
Not a silly question at all, and one that's seminal to understanding Irish politics in the pre and post WWI period.
An 'Orangeman,' briefly, is an Irish protestant Loyalist (i.e. Loyal to the English state) who derives the name from William of Orange...how William gets into this is one of the longer, more convoluted questions and refighting the Battle of the Boyne would be potentially controversial, but essentially the battle, fought on 1 July 1690, cemented British rule in Ireland up until the 20th Century. The Orange Order is a secret society based on the Masonic model.
Ireland by 1900 (and long before, as the recurrent uprisings and rebellions such as 1798 demonstrate) was divided into Nationalists - symbolised by the colour green - and Loyalists who were embodied in the traditions of the Orangemen. Both sides had societies, some public and others secret, such Orange societies (Lodges etc) on the Loyalist side. The groups devolved generally - but not exclusively - along Catholic/Nationalist and Protestant/Loyalist lines. There are ugly, confrontational traditions that exist in the North of Ireland to this day - the marching season with its triumphalist parades that breed sectarian violence, the middle-aged 'Apprentice Boys' etc.
Home Rule had long been a burning issue for Ireland and Irish politicians. The great Parnell, the 'Uncrowned King of Ireland,' had almost secured it in the previous century but was brought down by what Kenneth Griffith appropriately called 'bigoted moralists'. By 1912 the Liberals had managed to put it on the agenda again, and it seemed indeed it was imminent.
'Rome Rule' was the term used by the Protestant minority to describe 'Home Rule', as it was held that the Catholic church would be politically dominant under a home rule government. While the Roman Catholic Church certainly did hold a tremendous influence in Ireland, it should be remembered that some of the greatest of Irish patriots - men such as Wolfe Tone and Parnell - were Protestants.
Unfortunately for Anglo-Irish relations, the transition to Home Rule was suspended at the outbreak of war. It should be remembered that the concept was resisted furiously by the Protestant elite of Northern Ireland (although not by all - Lord Pirrie was a pro-Home Ruler), and they had already formed a private army, the 'Ulster Volunteers' - the British government turned a blind eye as this group began arming themselves. The Irish Nationalists in retaliation formed the 'Irish Volunteers', who were actively supressed. As an example of the different treatment meted out to these groups, at the outbreak of war the Ulster Volunteers were permitted to reform in their own combat regiments for the front, whereas the Irish Volunteers were dispersed. Many Irish Nationalists volunteered to fight for England on the battlefields of Flanders, hoping that they might win the respect and ultimately support of their comrades in arms. In addition, they hoped that as Britain was supposedly defending the right of Belgium against the Germans even marching across her, it was to be hoped that they would respect the right of Ireland to self government.
By 1916 they were disillusioned, hence the Easter Rising. This revolt was initially a dismal failure - the citizenry didn't side with the rebels, the rising was crushed and the leaders were shot. The shootings, however, finally swayed popular opinion behind the cause that men like Pearse, Connolly (who was so badly injured he had to be shot tied to a chair) and Clarke died for.
In the general elections of 1918 the population voted overwhelmingly for Sinn Fein candidates. Having won, they refused to take their seats in Westminster and instead convened an Irish Parliament, the Dail Eireann in Dublin. What followed was the Irish War of Independence (also known by such names as 'The Black and Tan War' after the British forces who were sent to supress the movement - my mother can still recount their atrocities), as the Irish people sought to fight for the self-government that had been withheld from them. Thanks largely to the brilliant leadership of Michael Collins - IMHO the most remarkable man who ever lived - the British were finally forced to the negotiating table in 1922. The Anglo-Irish treaty established an Irish Free State - the Irish had won self-government, but they still had to swear allegiance to the British Crown and, most tragically of all with ramifications that are still so bitterly felt today, the country was partitioned. The result was the Irish Civil war between the Free State forces and the Republicans who refused to accept the treaty, although it was overwhelmingly supported at a national referendum.
Michael Collins - one of those to lose his life in the civil war, shot by Republicans in an ambush - was eventually proven right in his statement that the treaty was not the freedom that all nations aspire to, but 'the freedom to achieve freedom.' Eventually successive Irish governments were able to use the concessions in the treaty to peacefully create today's Republic of Ireland.
Phew. Clear as mud, eh? But I managed to get through it all without mentioning the Curragh incident or even Cromwell...