Full Idea
A 'structure' in model theory is an interpretation which explains what objects some expressions refer to, and what classes some quantifiers range over.
Gist of Idea
A 'structure' is an interpretation specifying objects and classes of quantification
Source
Wilfrid Hodges (Model Theory [2005], 1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2
A Reaction
He cites as examples 'first-order structures' used in mathematical model theory, and 'Kripke structures' used in model theory for modal logic. A structure is also called a 'universe'.