In a historical context "Great Britain and Ireland" was a short version of the full name of the United Kingdom of Great Britain and Ireland.
The phrase Great Britain and Ireland is a term often used as a collective description covering the whole of the geographical area of the United Kingdom of Great Britain and Northern Ireland and the Republic of Ireland.[1][2][3][4] Similarly, it is often used geographically as a substitute or replacement for the term The British Isles, although it is ambiguous about the Isle of Man and the Channel Islands.
Many societies and social organisations are organised across Great Britain and Ireland, and use that term in their name. [5]
The phrase is also used in political contexts as a shorthand for the full names of the two states. Britain and Ireland is also used. Neither is formally correct. (see British Isles (terminology))
Unlike the term British Isles, it is almost entirely uncontroversial when used in a geographical sense e.g. "the weather is often wet and windy in Great Britain and Ireland".
The phrase "Ireland and Great Britain" is rarely used.