Jersey isn't part of the UK, but it's not exactly an independent country either.

If international diplomacy and constitutional law interests you, it's quite interesting.

Jersey is an autonomous, self governing Bailiwick and a Dependency of the Crown. It has an ISO country code and TLD, however the UK is responsible for representing the territory internationally in most cases, including at the UN. This is because the Crown delegates that responsibility to Her Majesty's Government. Jersey has no representation within the UK democracy itself and cannot sign international agreements independently, however it informally has relationships with lots of international bodies and other countries including the UK. Jersey has never been part of the EU and remains its own customs area. There are millions of other little warts and curious edge cases.

As someone from Jersey, I never quite know what to answer when someone asks what country I'm from.