Full Idea
The axiom schema 'Sentence "phi;" is true iff φ' is the (unrestricted) Tarski-Biconditional, and is motivated by the thought that if you are willing to assume or outright assert that φ, you will assert that φ is true - and also vice versa.
Gist of Idea
Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa
Source
Leon Horsten (The Tarskian Turn [2011], 02.2)
Book Reference
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.17
A Reaction
Very helpful! Most people are just bewildered by the Tarski bi-conditional ('"Snow is white"...), but this formulation nicely shows its minimal character while showing that it really does say something. It says what truths and truth-claims commit you to.