The force pushing on a surface divided by its area is known as a force per unit area, also known as pressure. Concerning the field of mechanics in engineering, the internal forces inside of an object due to any applied force divided by the area of the surface that force is applied is also called mechanical stress.
Pressure is a very important physical quantity in many situations. For example, the pressure needed on a blade to peel an apple is constant, so if a blade is sharper, it has a smaller area, and consequently, less force is required. If the blade were dull, then the area of the surface of the blade is larger, therefore requiring more force in order to get the same pressure and peel the apple. Another example of pressure involves snowshoes. If one was to use regular shoes to walk on snow, the pressure would be greater, causing the persons foot to sink in the snow, making walking difficult. Snowshoes work by increasing the surface area that is in contact with the snow, therefore reducing the pressure exerted by the person as he's walking and helping him or her to walk without sinking their feet in.