What pressure is
The sharp end of a nail drives into a board easily, while its flat head does not. The force is the same either way — what differs is the area the force is spread over. The quantity that captures that difference is pressure.
The definition of pressure
Pressure is the force acting on unit area.
pressure = normal force applied ÷ area the force acts on
Writing the force as F and the area as A, pressure = F ÷ A
Figure to be added
The word "normal" matters
The definition takes only the force applied normal to the surface — that is, perpendicular to it. If a force acts at an angle, only the part of it perpendicular to the surface contributes to the pressure.
The same force, different pressures
The smaller the area, the greater the pressure the same force produces. The sharp end of the nail drives in because that same force is landing on a tiny area.
On the next page we look at the unit this quantity is measured in, and at whether it carries a direction.