The best formal analysis of truth was discovered by Tarski in his semantic theory of truth. If a person ask me to give an exact statement of what "truth" is that would be my reply. Tarskis theory however does not cover truth as it is usually intended ("it is true the earth revolve around the sun").
As regard the later use of the word, to say a statement is true would in my oppinion mean it corresponds to reality in an objective sense. Philosophers, especially philosophers of religion or those without formal training, often go on to claim this definition preclude us from knowing what is true because we cannot "know" what correspond to reality in an objective sense and so e.g. science is a philosophical naive enterprise (some schools of postmodernism), or a naive enterprise without plugging in God somewhere (how God patch the problems is typically explained by exclaiming God can do everything or some such).
This is a confusion which arise because what we can have is confidence a proposition is true without knowing if it were true or not (indeed, if we knew, we would have either complete confidence in the statement or it's negation) and science operate on our confidence of statements. To say "X is true" then mean we are very confident X corresponds to reality; the confidence being at such a degree that in order to doubt the statement we should need to doubt just about everything else we know.
