A headstand is one of the most important poses in yoga. There are two reasons for it; both equally important.
On the physical level an inversion improves the circulation and lymph flow. Something good happens to the body when you turn it upside down and let the gravity work in the opposite direction. The positive effect is immediate. Tension in the shoulders and upper back releases, heaviness in the legs disappears, the face becomes rosy and nourished with a renewed blood flow and the digestive organs get a boost.
The second effect takes place in the energy canals. By regularly inverting the body stagnant energy becomes unblocked. Many illnesses, also those in the head, start slowly with an inadequate and restricted energy flow in the body. A headstand is an invaluable tool to maintain and improve mental health.
There is also an element of joy when doing headstands and inversions. The childlike - not childish - pleasure of seeing the world from a different angle is an exhilarating experience for a grownup. Joy keeps bitterness and cynicism at bay, leaving more space for higher feelings.
The ancient yogis cleverly figured out that a headstand a day keeps the doctor away. I wholeheartedly agree with this simple wisdom.