An 'empire' is a group of countries ruled over by a single monarch or ruling power. An empire doesn't need an 'emperor'. The British Empire comprised of Britain, the 'mother country', and the colonies, countries ruled to some degree by and from Britain.
The British began to establish overseas colonies in the 16th century. By 1783, Britain had a large empire with colonies in America and the West Indies. This 'first British Empire' came to an end after the American Revolution.
However, in the 19th century, the British built a second worldwide empire, based on British sea-power, made up of India and huge conquests in Africa.
The 'Whig' historians regarded the Empire as the deserved result of Britain's technological and moral, superiority. They were proud that 'a small kingdom' had amassed such a huge empire. By contrast, some modern historians such as Edward Said (1978) have criticised Britain's 'cultural imperialism', suggesting that it was based on nationalism and racist scorn for other people.