The British Isles is the most extensive of all denominations. It refers to all the islands located in northwestern Europe, including Ireland, the Isle of Man and the Channel Islands (Jersey and Guernsey).
The United Kingdom refers to the country governed by Queen Elizabeth. Ireland, the Isle of Man, Jersey and Guernsey are not part of the United Kingdom. What territories are included in the United Kingdom?: England, Scotland, Wales and Northern Ireland.
Great Britain is the biggest island of the British Isles. It doesn't include Northen Ireland, since this territory is in the island of Ireland. Great Britain includes Scotland, Wales and England.