Jersey is part of the British Isles. England, Scotland and Wales make up Great Britain, while the United Kingdom includes Great Britain and Northern Ireland. So, no, Jersey is not part of the United Kingdom.
Jersey is a British Crown Dependency and is defended and internationally represented by the UK government. Today, the Lieutenant-Governor of Jersey is the personal representative of Her Majesty the Queen here in the Island.
Jersey is self-governing and has it own financial and legal systems and its own courts of law.