The "displacement" field D is a 3D field, which models the initial tiny displacement of these particles, under the effect of gravity.
Basically, once that the scales of the initial perturbations induced by gravity are set ( which depends on the cosmological model), the rest of the evolution is set too:
particles start detaching or getting closer, depending on the amplitude of the initial displacement - which really looks like a tiny perturbation on a uniform distribution, at its start.