NH₃ has dipole-dipole interactions because the N atom in one molecule attracts the H atom of a nearby molecule.
A dipole-dipole interaction is the attraction between two polar molecules. When they approach each other, the negative end one molecule attracts the positive end of the other.
NH₃ is a polar molecule. The H is at the positive end.
The N atom is at the negative end because it is more electronegative than H and because it has at a lone pair of electrons.
The lone pair electrons at the 2-level are in a small volume. This gives a high density of negative charge.
The negative N atom of one molecule attracts the positive H atom of a nearby molecule. The molecules arrange themselves to increase their attraction and reduce their potential energy.
The dipole-dipole interaction in NH₃ is so strong that it has a special name — a hydrogen bond.