Gödel's Completeness Theorem states that in any consistent formal system, every statement that is true can be proven true using the system's axioms and rules of inference. This means that if something is logically valid, there exists a formal proof for it within the system. This theorem is significant in the field of mathematical logic and was established by Kurt Gödel in 1929. It highlights the relationship between syntax (formal proofs) and semantics (truth), ensuring that if a statement is true in all models of the system, it can be derived from the system's axioms.