A British person or object comes from the United Kingdom of Great Britain (England, Scotland, Wales) and Northern Ireland. It is sometimes used by the Isle of Man or the Channel Islands (near France). It can also be used for some overseas places like Gibraltar (near Spain) or the Falkland Islands (near South America).
The term "British" is often used to describe something unique to the UK, for example British people, 'the British way of life' or 'the British weather'.