Final answer:
The purpose of Congo red stain in capsule staining is to negative stain the background, thus making bacterial and yeast capsules visible as clear halos, highlighting a key aspect of microbial pathogenicity.
Step-by-step explanation:
The purpose of Congo red stain in capsule staining is to utilize a negative staining technique to visualize capsules around bacteria and yeasts. Since capsules do not absorb most basic dyes, the Congo red stain is applied to dye the background, but it does not penetrate the capsules. This results in the capsules appearing as clear halos around the borders of the cells. In this context, capsule staining is critical because it highlights the presence of a capsule, an important factor in determining a microbe's pathogenicity.