British English
British English refers to the dialect of the English language spoken in the United Kingdom. A popular sense of the term is that it means only the 'standard', typically written form of English in the UK and especially southern England. Linguists, however, would use it to mean any dialect, standard or not, that is used in England, Scotland, Wales and some communities in Northern Ireland, plus the UK territories surrounding the island of Great Britain. Often the accents of the UK are included in the definition too.
Spelling conventions
One reason that 'British English' might be associated with standard written language is that one of the most obvious differences between this and other varieties of English is its spelling conventions: colour rather than American English color, for example. These so-called 'British' spellings are however common in many other countries, generally those that were part of the old British Empire. Today, one aspect of culture shared between the Commonwealth of Nations countries is many of the spellings that predominantly originated in Britain: these are part of what is sometimes called 'Commonwealth English'.
Is 'British English' also 'Standard English'?
'Standard British English' - meaning the formal variety of UK English which is the subject of dictionaries and grammar books, and is taught in schools and to learners of English in the UK and in various places overseas - is just one form of British English today. Linguists would considers its study highly valuable, but other dialects would be equally worthy of study. Confining the definition of 'British English' to the standard variety also creates a problem: all forms of a living language change all the times, as new generations develop new vocabulary or reanalyse one aspect of their native language's grammar in a slightly different way from how their parents used it. This also applies to the 'standard' language, though this process is typically slowed by its being codified in a set of written conventions and prescriptivist grammar rules. If linguists were to agree with the popular definition of British English as standard English, new innovations would go uncatalogued and linguistic diversity could not be used as data to further our understanding of language itself.