Truth is something that squares with reality. When you are sworn in to give testimony in a U.S. court of law, you promise to "tell the truth, the whole truth, and nothing but the truth."
When you're cutting to the heart of something, you might start a statement with, "The truth of the matter is..." or "To tell the truth..." When you hear these introductory phrases containing truth, reality is supposed to follow. The American comedian Stephen Colbert coined the term truthiness as a satirical poke at politicians and pundits whose claims often have no basis in reality. Truthiness is what you wish were truth — unconstrained by fact or logic.