Full Idea
Anyone who accepts the notions of whatever object language is in question - and this can be chosen arbitrarily - can also understand 'true' as defined by Tarski for that object language.
Gist of Idea
In Tarski's definition, you understand 'true' if you accept the notions of the object language
Source
Hilary Putnam (Meaning and the Moral Sciences [1978], Intro)
Book Reference
Putnam,Hilary: 'Meaning and the Moral Sciences' [RKP 1981], p.2
A Reaction
Thus if we say "'snow is white' is true iff snow is white", then if you 'accept the notion' that snow is white in English, you understand what 'true' means. This seems to leave you with the meaning of 'snow is white' being its truth conditions.