Asperity is defined as unevenness of surface, roughness, ruggedness (OED). Flat surfaces, even those polished to a mirror finish, are not truly flat on an atomic scale. They are rough, with sharp, rough or rugged outgrowth, termed asperities.
When two macroscopically flat surfaces come into contact, initially they only touch at a few of these asperity points. These cover only a very small portion of the surface area. Friction and wear originate at these points and thus understanding their behavior is important when studying materials in contact. When the surfaces are subjected to a compressive load, the asperities plastically deform, increasing the contact area between the two surfaces until the contact area is sufficient to support the load.
The Archard equation is a simplified model of asperity deformation when materials in contact are subject to a force.