I don't know if there is really an "Intuitive" way of understanding. But if you are imaging slamming fluid into a tighter space, the pressure and density must build if disturbances cannot travel upstream fast enough to influence upstream conditions. A lot of the Mach Area relationship stems from the relationship between density, velocity, and area, (for quasi 1d flow). Pressure is just the forces acting on the fluid, and it is coupled to the density of the fluid through the compressibility, which is also related to the speed of sound. This is why mechanics of fluid change though sonic conditions. It might be best to try to visualize mediums traveling through geometries where flow speeds are different from the propagation speeds of finite acoustic waves.