Azurophilic granules exhibit a characteristic reddish-purple color when stained with azure dyes, such as in the Wright-Giemsa stain. This property makes them easily identifiable under a light microscope, aiding in the diagnosis of various blood disorders and infections. The staining process involves the use of eosin and methylene blue, which differentially stain cellular components, highlighting the granules against the cell's cytoplasm.