Prescriptivism (/prəˈskrɪptɪvɪzm/) is an approach to linguistics in which a language authority decides 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.
Nearly all modern linguists follow the opposite approach, i.e. descriptivism. However, there is somewhat of a middle approach which notes prescriptions and proscriptions but does not endorse them per se, and leaves it up to the language user to decide on what language they wish to use.
There is an influence of politics here as well. Conservatives, as traditionalists and conformists, tend to decry language change, and argue for use of formal language based on edicts from language authorities. Liberals tend to be more accepting of non-conformity and language change, however they tend to make judgements based on political correctness, and prescribe use of inclusive language (e.g. gender inclusive language).
Many prescriptive linguists cannot agree on "the rules". One advantage of prescriptivism is that although the rules given may not be accurate, they can be clear. Sometimes, that clarity may be more useful to language learners than accuracy.
Compare descriptive grammar -- descriptivism.