An arbitrary
set of dictatorial
rules purporting to govern the
linguistic syntax of speech and/or writing. A
prescriptive grammarian would, for example, find fault with me for ending the next sentence of this writeup with a preposition, and for beginning it with what (s)he terms a 'conjunction'. But if this sentence is as comprehensible as the previous one, what would I want to phrase it differently for?
While the prescriptive-English grammarian will usually reply that standardization of English is essential to communication, the truth is that support for prescriptive grammar is born from intellectual snobbery and classism. In practice, even the daily speech of such snobs is rife with gross violations of their touted rules, and yet, effective, highly-precise, unambiguous communication still occurs. Moreover, common speech has very complex, communication-enabling, ambiguity-eliminating rules thankyouverymuch. These rules are informally but quite solidly learned and mastered as early as age 2. It is these rules that are the basis of the only true grammar system.
Scholarly linguists aim to study, document and reflect, (among other things), the surface-grammar rules which manifest in language. They are interested in studying the language as it is spoken. Meanwhile, others in Academia (and those who esteem them) aim to "correct", refine, and prescribe a language which is not actually spoken by anyone.