Magnesium and constipation are directly related because the entire digestive tract is essentially a long smooth muscle, and magnesium is a muscle relaxant.

For any digestive process to take place properly, the muscles of the digestive system need to be able to relax and contract.

Also, when your magnesium intake is optimal, there is an increase in intestinal water content, which helps with the initiation of peristalsis- the wave-like motion which moves food through the intestines.

Additionally, magnesium is necessary for the production of hydrochloric acid (HCL), the secretion of digestive enzymes by the pancreas, and the protection, repair, and regeneration of the organs of the GI tract (esophagus, stomach, pancreas, liver, gallbladder, small and large intestine).

A good and easy-to-understand article about magnesium is this. It explains about constipation also.