A normal, untreated, reflective wall would treat a sound reflection like a billiard ball banking off the table. All the normal physics of this interaction apply; the angle of incidence is the same as the angle of reflection, so the billiard ball bounces off the table, moving in a predictable direction based on its initial trajectory, and emerges from the reflection relatively unscathed (ie, it’s still the same billiard ball).
But what if we put up a diffusor at the reflection point, so the billiard ball hits the diffusor? Well, if the diffusor is working correctly, then the billiard ball will explode into multiple fragments, with each fragment fanning out evenly in its own direction relative to the reflection point. This is spatial dispersion; the billiard ball fragments are scattered evenly in all directions (across the 180 degree plane of the diffusor).