Ireland's provinces can be a confusing issue - there are technically four Irish provinces, but there was a fifth province ... and isn't Northern Ireland (which is a seperate country that is a part of the United Kingdom) called a province as well? Let us sort some of the misconceptions out.
Connacht, the North-West
Connacht (in older documents also called “Connaught”, in Irish Cúige Chonnacht) consists of counties Galway, Leitrim, Mayo, Roscommon, and Sligo. It is the smallest province of Ireland if you go by the number of counties included. Connacht is often described as the West of Ireland, and for the most part, it lies on the Atlantic seaboard - though Roscommon is a landlocked county and does not have access to the sea (Leitrim's status is a bit debatable too).
The name of the province denotes that it is “the Fifth owned by the Descendants of Conn”. Today 550,742 people reside in Connacht (according to the census of 2011)6
The geographical borders of Connacht are (roughly) the Atlantic Ocean from Galway Bay to Donegal Bay, parts of the Shannon in the east and the Burren to the South.
Leinster, the East
Leinster could be termed Ireland's East, including large swathes of the Midlands too. The counties of Carlow, Dublin, Kildare, Kilkenny, Laois, Longford, Louth, Meath, Offaly, Westmeath, Wexford, and Wicklow are parts of Leinster - thus making Leinster the largest province because it includes one-third of all of Ireland's 32 counties. The Irish name of the province is Cúige Laighean or Chúige Laighean, literally means “the Fifth owned by the Laigin tribe” (the simplified and Anglicised Leinster simply means “the Land of the Laigins”).
Leinster is the most urban province of Ireland – Bray, Drogheda, Dublin, Dundalk, Dún Laoghaire, Kilkenny and Wexford are major Irish towns and cities found here. No less than 2,630,720 people live in Leinster (according to the census of 2016), reflecting a population growth of around 35% over the last twenty years.
Traditionally, Leinster was the center of Anglo-Norman and later British Ireland, starting with first settlements and extending into the Pale - an area of around 1.500 square kilometers tightly ruled from Dublin. The rest of Ireland is, literally "beyond the pale."
The geographical borders of Leinster are (roughly) the Irish Sea and St.George's Channel, the Rivers Suir and Shannon, the lakelands and drumlins of Cavan and Monaghan, and Carlingford Lough.
Munster, the South-West
Ireland's province of Munster, in Irish Cúige Mumhan or Chúige Mumhan, is mainly defined as the South-West of Ireland. It was home to (and thus “the Fifth”) of the followers of Mumha - who was either a warrior queen, or a goddess, or maybe both. As Munster originally consisted of three major kingdoms (Thomond, Desmond, and Ormond) it still has three crowns in its flag.
Encompassing the counties of Clare, Cork, Kerry, Limerick, Tipperary (the only landlocked county), and Waterford, Munster is often considered one of Ireland's most desirable and beautiful spots. Because of this, it is the Irish province most popular with tourists (if you disregard Dublin). Inhabited by a population of 1,280,020 (according to the census of 2016), a population growth of around 23% over the last twenty years is mainly due to influx into the urban centers (Cork, Limerick, and Waterford) and the Shannon Area (known as the home of many a multinational company).
The geographical borders of Munster are (roughly) the Atlantic Ocean, the Suir and the Shannon and the Burren.
Ulster, the North-East
The province Ulster (in Irish “Cúige Uladh“, in Ulster-Scots “Ulstèr“, literally “the Fifth of the Uladh”) consists of nine counties - six of which form Northern Ireland, three being part of the Republic of Ireland. Note that Ulster is not the same as Northern Ireland, though it is Ireland's North (with the quirky fact, remember this for the pub quiz, that the northernmost part of Ireland is not in Northern Ireland). On the other hand ... all of Northern Ireland is in Ulster.
Ulster consists of the counties of Antrim, Armagh, Cavan, Derry, Donegal, Down, Fermanagh, Monaghan, and Tyrone. Antrim, Armagh, Derry (or, if you prefer, Londonderry), Down, Fermanagh and Tyrone are Northern Ireland - Cavan, Donegal and Monaghan are part of the Republic. Ulster is the place where the most famous Irish epics take place - like the epic “Cattle Raid of Cooley“ (sounds quite like rural petty crime, but it definitely isn't just that).
The geographical borders of Ulster are (roughly) the Irish Sea, the North Channel, the Atlantic Ocean and the lakelands and drumlins of Fermanagh, Cavan, and Monaghan as well as Carlingford Lough.
More information on Ulster:
Introducing the Province of Ulster
The Best Things to See in Ulster
Northern Ireland, a Part of Ulster and the United Kingdom
Northern Ireland is an artificial product of the partition - and thus can safely be left out if you discuss the provinces of Ireland. There is, however, a tendency in media to report from "the province". This is a non-historical usage of the term and usually reflects the same inaccuracy that will, time and again, equate Northern Ireland with Ulster.
For all intents and purposes, Northern Ireland is NOT a province of Ireland (and, having mentioned that, neither of the United Kingdom or Great Britain or England).
Finally, there once really was a "Fifth Province of Ireland", which brings us to the last point on "The Middle."
An Mhi, "The Middle"
Ireland today consists of the Provinces of Connacht, Leinster, Munster, and Ulster – in ancient times, however, a fifth province really existed. This also explains the original name of the provinces, which all refer to “the Fifth”.
The fifth province was simply called "the Middle", in Irish an mhí - today this name is used by both Counties Meath and Westmeath, they would roughly conform with the borders of the ancient fifth province, the seat of the High King (which also explains Meath's nickname “the Royal County“).
Purists might argue that the fifth province of Ireland wasn't quite in the middle.