Hertzian contact stress refers to the localized stress that occurs when two curved surfaces come into contact, such as two cylinders. This stress is critical in determining the performance and lifespan of mechanical components like bearings. The discussion emphasizes the importance of calculating contact pressure and understanding deformation under load to prevent failure. Key factors influencing Hertzian stress include material properties, surface roughness, and the geometry of the contacting bodies. Accurate analysis of these stresses is essential for reliable engineering design and maintenance.