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!

Read another response by Nicholas D. Smith
Read another response about Truth