Full Idea
A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc.
Clarification
The Cartesian Product produces all permutations of pairs of objects
Gist of Idea
A model is a domain, and an interpretation assigning objects, predicates, relations etc.
Source
Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3)
A Reaction
The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts.