From Teflpedia

Prescriptivism is a perspective on language in which an authority figure decides on what language is acceptable and hence subject to prescription and what language is erroneous and therefore subject to proscription. Prescriptivism mostly covers grammar, but it can also cover semantics, punctuation, etc.

Formal registers are often more prescriptivist than informal registers.

Nearly all modern linguists follow the opposite approach, i.e. descriptivism. However, there is somewhat of a middle approach which notes proscriptions but does not endorse them per se.

Many prescriptive linguists cannot agree on "the rules".