Full Idea
A specification of a domain of objects, and of the rules for interpreting the symbols of a logical language in this domain such that all the theorems of the logical theory are true is said to be a 'model' of the theory.
Gist of Idea
A 'model' of a theory specifies interpreting a language in a domain to make all theorems true
Source
Michal Walicki (Introduction to Mathematical Logic [2012], History E.1.3)
Book Reference
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.33
A Reaction
The basic ideas of this emerged 1915-30, but it needed Tarski's account of truth to really get it going.