The word British has several different uses. See the article on Britain for more details on the development and use of the word Britain.
In a geographical context, it usually applies to a person or object from, or the people or nation of ("the British") the island of Great Britain—though, confusingly, the term "British Isles" is commonly used to include also the (non-British) island of Ireland. The term "Briton" is increasingly used to describe a British citizen. Sometimes it applies to an area or territory currently or formerly under British rule, for example the British Virgin Islands, the British Indian Ocean Territory or British Columbia, now a province of Canada.
In an historical context, it refers to a territory or person with allegiance to the British Empire. (This usage of the word may be controversial, since many subjects of the empire were included in it by force and did not have any allegiance to it.)
In an ethnological context, it refers to the Brythonic people who once inhabited much of Great Britain, and a person of British descent either resident in the United Kingdom or abroad.