You need to remember that pressure represents the force per unit area, hence, when an atom or a molecule springs off of a surface, a force is exerted. The group of all collisions between atoms or molecules and surfaces leads to pressure. The collision between an atom or molecule and a surface, leads to a change in momentum. The change in momentum produces an impulse force, which is equal to momentum change divided by collision time.
Pressure resulted from the multiple elastic collisions between atoms and surface is equal to the average of the sum of bouncing forces exerted by the surface per unit of time.
The pressure is increased if the collisions occur oftenly, while if collisions occur rarely, then the pressure is decreased. For example, the pressure of gases is increased if the temperature is increased, since the higher the temperature is, the faster the atoms and molecules move.