The United Kingdom of Great Britain and Ireland was the formal name of the United Kingdom between 1801 and 1927. In 1922, the majority of Ireland seceded to form the Irish Free State. The Royal and Parliamentary Titles Act 1927 amended the name of the Parliament of the United Kingdom to reflect the change in the country's boundaries, and the Act is conventionally considered to mark the point when the name of the state changed as well.
The United Kingdom of Great Britain and Ireland came into being on 1 January 1801 under the terms of the Acts of Union 1800, by which the formerly separate kingdoms of Great Britain and Ireland were united. The Kingdom of Great Britain had itself been formed in 1707 by the union of the formerly separate kingdoms of England and Scotland.
In 1919, the majority of Irish MPs refused to recognise the Parliament of the United Kingdom and formed a unilaterally independent Irish parliament, Dáil Éireann, with an executive under the President of Dáil Éireann, Eamon de Valera. A War of Independence was fought between 1919 and 1921. Finally in December 1922, twenty-six of Ireland's counties exited from the United Kingdom of Great Britain and Ireland and formed an independent Irish Free State. The southern part of Ireland that seceded from the union is today the Republic of Ireland. It covers the same territory as the Free State, but adopted a new constitution in 1937.
Six counties of Ireland, called Northern Ireland, remained a part of the continuing United Kingdom, which was renamed the United Kingdom of Great Britain and Northern Ireland in 1927, in accordance with the Royal and Parliamentary Titles Act 1927. The present-day United Kingdom retains the same constitutional and parliamentary systems but covering only a portion of the previous territory.
Despite being a kingdom in its own right, Ireland before 1801 did not have full sovereignty. The Kingdom of Ireland was a settler state, with the King of Ireland being the same person as the King of England (and, since the 1603 ascension of the Stuart dynasty, the King of Scotland). Its government was headed by a Lord Lieutenant and his Chief Secretary, who were responsible to the government of Great Britain rather than to the Parliament of Ireland. Before the Constitution of 1782, the Irish parliament was also severely fettered, and decisions in Irish courts could be overturned on appeal to the British House of Lords in London.