Full Idea
The symbol in 'I |= S' reads that if the interpretation I (about word meaning) happens to make the sentence S state something true, then I 'is a model for' S, or I 'satisfies' S.
Gist of Idea
|= should be read as 'is a model for' or 'satisfies'
Source
Wilfrid Hodges (Model Theory [2005], 1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.1
A Reaction
Unfortunately this is not the only reading of the symbol |= [no space between | and =!], so care and familiarity are needed, but this is how to read it when dealing with models. See also Idea 10477.
Related Idea
Idea 10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]