The 'British Isles' are made up of many islands including the 'Isle of Man', 'Ireland' and the larger 'Great Britain' which is divided into England, Scotland and Wales. The 'United Kingdom of Great Britain and Northern Ireland' is the three countries on the island of Great Britain and a small part of Ireland called 'Northern Ireland' not including the Isle of Man. The rest of the island of Ireland is the independent 'Republic of Ireland'.
Note. The name Britain (not Great Britain) is often used as a short name for the country. Since 1922 the correct name of the country has been the "United Kingdom of Great Britain and Northern Ireland", but by 1922 the phrase "Great Britain" was in widespread popular use and has since become synonymous with anything/anybody representing the "United Kingdom of Great Britain and Northern Ireland".
Therefore the term "Great Britain" is sometimes used erroneously to mean the "United Kingdom of Great Britain and Northern Ireland". The name for the country at major international sporting events has never been corrected and it still often competes as Great Britain and Northern Ireland. Note also that the Isle of Man and the Channel Islands are Crown Dependencies, not technically part of the UK (or of the EU).
These are generally included in the expressions Britain or Great Britain.
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