The study of interpretations of language.

In mathematical model theory, a set of sentences in a Formal language is called a theory; a model of a theory is a structure (e.g. an interpretation, i.e. something) that satisfies the sentences of that theory. By definition of sentences, we are considering formal languages which are Formal systems, typically Logics

The nonlogical symbols in the formal system (variables, constants, functions, operators, etc) are called the signature. A model for the system should have the same signature, that is, give an interpretation to the symbols in the signature of the language.

https://plato.stanford.edu/entries/model-theory/

See also finite model theory