The eyes are made of the same spongy matter as the brain, and they develop at the same time as the brain when we are in the womb. Our perception about the world is largely formed through our eyes, as we take in 80% of our information about the outside world through them. One might say that the eyes are truly an extension of the brain. Knowing some things about the eyes and their connection to the brain can help in the effort to find mental and emotional balance.
Eye movement to the right indicates and stimulates left-hemisphere brain activity (logic, sun, masculine, time, analytical), while eye movement to the left indicates and stimulates right-hemisphere brain activity (analogic, moon, feminine, spacial, tone, voice). Both hemispheres provide equally valuable functions, and we are happiest when they are working equally and together.
If you tend towards anxiety, watch out for looking up excessively as this creates further stimulation. If you tend towards depression, avoid closing your eyes or looking down too frequently.
The "Drishti", in the yoga practice, is a point of focus where the gaze rests during asana and meditation. Focusing on a drishti significantly aids concentration. When the eyes are wandering, they are feeding the brain various bits of information, which manifests as random, unconscious memory associations, thereby feeding the mental chatter.
Many yoga poses have a specific drishti and the correct drishti will help you find the depth or alertness that the pose is calling for. For instance, in Parsvakonasana and Trikonasana, the gaze is towards the raised hand. In forward bends, looking down can help with deeper flexion as looking down has a relaxing effect. Or, in spinal twists, looking down and exhaling can help increase cervical rotation.
When working with a drishti, keep in mind that even though a drishti is a fixed gaze, the eyes should always stay soft, never straining. This relaxes the brain and therefore the rest of the body. From this calm place with less mental chatter, we can make healthier decisions more easily. In a relaxed state, we are more able to enjoy what we have and what we are doing.