I'm a bit of a semanticist, and my take on truth is the following, not representative of anyone else's.
Truth and falsity are just values distinct from one another, that can be represented however you like: classically, 1/0 or T/F. They have no significance beyond the fact that they are distinct from one another. Using this binary distinction, you can build a truth-conditional semantics (bracketing issues of non-classical truth values, truth value gaps, truth value gluts, fuzzy truth values, and so on).
A semantics for a language is just an abstract set of ideal rules that can be mathematically modeled for interpretation, much in the way that an artificial language can be semantically parsed or interpreted. In this state, it has no real-world application, but nevertheless various real world linguistic
practices can be seen as implementing this abstract structure for certain ends, just as when one plays a game like chess, one employs a mathematically describable set of rules, but these rules themselves are not tied to the playing of any particular game, or the employment of any particular strategy. (And the semantics of natural language are far, far, far more complicated than any deliberately constructed game, just as a fact of nature and because, well, it's natural, not artificial, and so the rules manifest without stipulation, and so are never completely precise and never set in stone, always eluding complete formulation).
Truth and falsity simply function as binary values within this abstract set of rules. They do not have any pragmatic significance. Where they gain their significance is when you plug them into some linguistic practice that makes
use of these binary values for various ends. So, for example, there is a presumption that one
tells the truth, and so an assertive speech act in some sense privileges one value of this binary over the other, and makes it the goal of assertion. Within this pragmatic framework, these mere abstract binary values are imbued with useful sense inside of a linguistic community, and we allow ourselves to conduct our behavior meaningfully and systematically in such a way that the 'yes'/'no' difference gets involved in all sorts of intersecting conventional practices.
Semantically, truth is nothing but this binary opposition to falsity; in actual practice, it is nothing but what this binary opposition is put to use for in the employment of the language's abstract mechanics according to a certain way of speaking (just as two people can play chess with the same abstract rule set, but with different meta-game strategies, and even with entirely different goals in mind: one can still be playing a legal game of chess while
trying to lose, for example, instead of trying to win; and trying to win is something like trying to tell the truth in this analogy).
In real life the abstract semantic system that governs linguistic usage doesn't float freely of course, but is always embedded in some pragmatic use of language. The point is, though, that any such use emergently manifests a regularity in semantic behavior that is
in turn describable by such an abstract set of rules, and in particular making important use of a certain binary attaching to the semantic valuation of a privileged syntactic class of linguistic vehicles used for utterance: sentences. Thus, sentences have a truth value, they are either true or false (or rather, utterances of these given a context and appropriate parameters of evaluation are). And then we can imagine this abstract set of rules being applied to foreign uses, if we please.
Therefore to ask what truth and falsity are is just to ask for a description of the semantics of the language as a whole. When we do the work of semantics, we are already describing truth and falsity in so doing: there is nothing
else to do once this work is finished. It is a semantic question, for linguistics, and not for philosophy (although what I have just told you is a philosophical, and not a linguistic, position). So to see how truth and falsity function in a current semantic theory, one need only learn that theory. In classical Montagovian semantics, they act as binary values that exhaust the domain of a fundamental semantic type: so-called type t. And semantically meaningful bits of languages are in turn compounded to create syntactic objects of a certain type, viz. sentences, which in turn have a truth value as their denotation. The theory
shows how truth and falsity function, and is implemented once a pragmatics is given. To the extent that such a pragmatics combined with our semantics results in a realistic model of linguistic behavior, we have explained what it is that truth and falsity are.
Hence the charge that the Wittgensteinian maxim is ignored is misplaced: truth-conditional semantics does not in principle divorce meaning from use, in describing meanings as certain mathematical objects, because the whole point is that the
use of language can be mathematically described in conjunction with a pragmatics. Semantics should no more be a philosophy of action, or provide one, than a rule book of chess should explain the optimal way for white to open. And to complain that a rule book of chess only mathematically defines well-formed games of chess according to legal moves of pieces, to say that it was inappropriate or mistaken because it did not tell you how the player is to supposed to win, or what strategies people typically use, is equally absurd.
Also, there is definitely, definitely truth in fiction; and aside from that, massive amounts of everyday use do deal with the exchange of information,and to pretend otherwise seems disingenuous. And finally, even where it does not, the purposes of the conversation use truth-conditional vehicles to make their point, and the point they are trying to make
would not make sense if this were not so. If I don't understand the conditions under which 'you look nice today' is literally true, I cannot make sense of how a sarcastic utterance of this same sentence intends to subvert those conditions.