"Standard English" is a term used to refer to the kinds of writing, speaking, and pronunciation of English that are generally accepted as the "norm" or as the preferred forms in an English-speaking country. It is often associated with an educated use of the language, grounded in what has been traditional and conventional. It tends to be the kind of English taught in schools and sanctioned by educational authorities. In the English-speaking countries, there tend to be no formal, recognized bodies established to define or determine what counts as "standard English." Nevertheless, there has usually been a fairly wide consensus about what is proper and improper use of English and what is grammatical or ungrammatical English usage. Of course, actual ideas about what should or does count as "standard English" are open to debate. The English language also has a long history of evolving in ways so that what once seemed unacceptable was later accepted as part of the conventions of "standard English."
In a particularly valuable article (linked below), the noted scholar of language David Crystal succinctly defines "standard English," quite simply, as
the variety of English which carries most prestige within a country.
For a very famous discussion of what constitutes (or should constitute) good English usage, see the article by George Orwell linked below.
Finally, for a famous handbook on good English usage, see the link below to Strunk's The Elements of Style.