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. Some historians point to the positive legacy of British rule, with formal systems of government, law and education as well as the development of infrastructure, like railways. However, others argue that this view can overlook the more shameful aspects of Britain’s past. These include the extensive use of slavery (in 17th and 18th centuries), the loss of land and culture of the native people (Aborigines in Australia) as well as deaths caused by famine (in India 1943) and violence (in Kenya in the 1950s).