Same amount of force acting on a given surface produces different effect (result) depending upon the surface area of contact with with the force is applied. Consider following situation. Even if same force is applied by the person the bowling pin on the left hand side doesn't penetrate the wood but the nail on the right hand side very easily penetrates the wood. There are two factors that determines the penetration first is force and the second is the surface area.
So, the pressure is defined as "the force acting perpendicularly per unit area". It is measured in N/m2 which is also called pascal. 1 Pascal is the 1 Newton force applied in 1 m2 area perpendicularly.