Perhaps this is the most commonly recognized hand mudra. While teaching at a rural school house in Costa Rica, I asked the youngsters what yoga was. Several of them closed their eyes and placed their hands on their knees in gyan mudra. When I asked where they learned that, they responded, “television.”
It is particularly common to see practitioners meditate with gyan mudra. According to Indu Arora, http://www.yogsadhna.com/, a leading expert on hasta mudras in the U.S., gyan mudra is particularly useful for balancing vata (air and ether). Since most doshic imbalances have some degree of excess vata, it makes sense that this is a widely implemented hand mudra.
As explained on another page, http://thenamastecounsel.com/prithvi-or-surya-mudra-earth-or-sun-mudra/ each finger represents one of the five elements. The thumb is commonly related to agni, or fire, which regulates digestion and the index finger is air.
Additionally, the tip of the thumb is associated with the pressure points for endocrine and pituitary glands.
Arora says this mudra helps eliminate lethargy, dullness of mind, and loss of memory. The author of a beautiful book on mudras acknowledges that when the thumb and forefinger are touching, it begets a sense of peace and harmony in the body and mind. Both of which are essential to meditation. “It takes 30 seconds to just “ignite” the mudra, to create the electromagnetic circuit. Then, it needs to be held for at least two minutes, but you can hold it for as long as you can, ideally for 45 minutes in a 24 hour period.”