The Isle of Man is an internally self-governing dependent territory of the British Crown or "Crown Dependency" and it's people are British citizens. It is not a part of Great Britain or the United Kingdom. However, Her Majesty the Queen is the Head of State and is known as the Lord of Man. Her personal representative on the Island is His Excellency the Lieutenant Governor. The Crown appoints a new Lieutenant governor every 5 years.
As a Crown Dependency the Island is completely autonomous in legislative,executive and judicial matters. However the UK is ultimately responsible for the Island's defence and international relations.
The Isle of Man is not a member of the European Union but it does have a special relationship with the Union through an agreement know as "Protocol 3" to the UK's Act of Accession to the European Community. This allows the movement of people. However the Isle of Man neither contributes to, nor receives funds from the European Union.