Could you please recommend about some books or paper which deals with the question of the meaning of being true? I mean - What does it mean to say about something that it is true?

Both the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy have good articles on truth. Two books I would recommend that get into some related issues would be: Bernard Williams, Truth and Truthfulness (Princeton 2002) Simon Blackburn, Truth: A Guide (Oxford 2005) Hope this helps!

Is it conceivable that there are truths about science, nature or the universe that we are better off not knowing? What might some such truths be?

There have recently been psychological studies showing that people tend to have somewhat inflated views about themselves in terms of their own attractiveness. Those whose self-images most closely mathced other people's actual assessments of them tended to be depressed. So that is one example. Another comes from Greek mythology (see Aeschylus's Agamemnon from his trilogy, the Oresteia ). Cassandra seduced Apollo, and promised to have sex with him if he gave her the gift of prophesy. He agreed and gave her that gift, but then she reneged on heer part of the deal. So Apollo added the curse that no one would ever believe Cassandra's prophesies. Cassandra "sees" that she (and her captor, Agamemnon) are about to be mercilessly slaughtered in his home. But there's nothing she can do about it, and no one will listen to her when she wails out her terrors... There's an old blues song that goes, "Nobody loves me but my mama...but she may be jivin', too." So there's another option for you!

Do you think it's possible, even theoretically, for there to exist a substantive belief (any kind, about anything) that is impervious to any argument, cannot be debunked, etc., and yet is false?

Yes, at least theoretically. An example of how this might be is given in the first of Descartes' Meditations on First Philosophy. Descartes asks us to consider a world that is governed by a kind of evil god who delights in nothing more than making us believe what is false. In such a world, we would be able to find no evidence at all to debunk the falsehoods to which the god inclined us. Descartes challenges us to see if we can be absolutely sure that we do not actually inhabit such a world! Modern popular culture has taken up this scenario in various entertaining ways. I think it is fair to say that the worlds imagined in "Total Recall," and "The Matrix" are excellent examples of scenarios that raise the theoretical possibility of false belief that is (at least for those who don't escape the Matrix!) invulnerable to refutation.