The pressure of a fluid can be explained microscopically in terms of molecules bouncing off the walls of a container. The molecules have a certain mass and speed, so when they bounce they transfer a certain momentum to the wall; and since a certain number of bounces occur per unit area and time, the averaged-out result of all the bounces is pressure. So the pressure depends on the speed (temperature) and density of the molecules.
If we consider an incompressible fluid, however, we can apparently alter the pressure without changing the temperature or density. Suppose we have a container of fluid and apply force to it using a piston. Since it's incompressible, the piston doesn't move, so the density doesn't change; no work is done on the fluid, so we can't heat it up. Nevertheless the force is transmitted through the fluid "somehow" and results in an increase in pressure. A large force will cause a large increase in pressure.
Evidently the approximation of a perfectly incompressible fluid breaks down here. Pushing on it with a piston must slightly change the density, temperature, or both. How does this work? How do slight changes in these properties result in a large change in pressure, microscopically?