The official title of the UK is "The United Kingdom of Great Britain and
Northern Ireland". Ireland is composed of four Provinces - Leinster,
Munster, Connaught and Ulster. Prior to 1922 all of Ireland was part of
Great Britain but a treaty in that year ceded all but Ulster to the
Irish as an "Irish Free State". Ulster became "Northern Ireland". In
1937 the Irish Free State became Eire and in 1949, The Republic of
Ireland. The continuing "troubles" between Ireland and Britain stem from
the fact that some in Ireland think Ulster should be part of the
Republic and a small minority are prepared to resort to violence and
terrorism.
Sorry to confuse people and drag out the thread with even more information, but the historic Irish province of Ulster was composed of 9 counties. When Ireland was partitioned, 6 of the counties of Ulster composed Northern Ireland and remained under British rule, while the other 3 became part of the Irish Republic (or as it was then, the Irish Free State). Thus the usage of 'Ulster' and 'province' in the political rather than the geographic and historical sense is a kind of shorthand for 'most of Ulster' and 'most of the province'.
Ed.