Realizability is a concept in mathematical logic and computer science that connects formal theories with computational processes. It suggests that a mathematical statement can be considered true if there exists a computational method to demonstrate its truth. This idea helps bridge the gap between abstract mathematical reasoning and practical computation. In the context of constructive mathematics, realizability provides a framework for understanding how mathematical objects can be constructed or computed. It emphasizes the importance of explicit examples and procedures, making it a valuable tool in areas like type theory and proof theory, where the focus is on the constructive aspects of mathematical proofs.