Posterior (Dorsal) Primary Rami

What does ventral rami do?
Ventral rami (also called anterior primary rami) of the cervical and lumbar region supply the muscles and skin of the upper and lower limbs through brachial and lumbar plexuses respectively. The ventral rami of the thoracic region supply the abdominal muscles and skin on the anterior and lateral aspect of the trunk.
What does dorsal rami do?

Generally they supply the muscles and skin of the posterior part of the trunk with the exceptions of those of C1, S4 and S5. Dorsal rami remain distinct from each other, and each innervates a narrow strip of skin and muscle along the back, more or less at the level from which the ramus leaves the spinal nerve.