The internal pressure is the contribution from intermolecular interactions that tends to reduce the pressure of gas relative to the pressure one would expect for an ideal gas. As the figure above shows we can imagine this reduction arising from the interaction of all nearby molecules pulling on a molecule approaching the wall of a container and thereby reducing its momentum. By reducing the momentum of the particle as it strikes the wall the force is also reduced and therefore the pressure is reduced. The point here is that we can use the machinery of the exact differential to find an way to calculate the internal pressure.