Great Britain is not a country—it's an island. This is a common misconception.
Great Britain = the largest island of the British Isles, containing three countries:
United Kingdom of Great Britain and Northern Ireland (UK) = the sovereign nation comprising:
Great Britain = geographic island (3 countries).
United Kingdom = political state (4 countries).
Northern Ireland is part of the UK but not part of Great Britain (it's on the island of Ireland).