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Full Idea
In Tarski's theory of truth, although the notion of truth is applicable only to closed formulas, to define it we must define a more general notion of satisfaction applicable to open formulas.
Gist of Idea
Truth only applies to closed formulas, but we need satisfaction of open formulas to define it
Source
comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by John P. Burgess - Philosophical Logic 1.8
Book Ref
Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.9
A Reaction
This is a helpful pointer to what is going on in the Tarski definition. It culminates in the 'satisfaction of all sequences', which presumable delivers the required closed formula.