Dangma is a Tibetan term for "a purified soul," thus the eye of dangma is a reference to the spiritual sight of the elevated initiate.
"In India it is called "The Eye of Siva," but beyond the great range it is known as "Dangma"s opened eye" in esoteric phraseology. Dangma means "a purified soul," one who has become a Jivanmukta, the highest adept, or rather a Mahatma. His "opened eye" is the inner spiritual eye of the seer, and the faculty which manifests through it is not clairvoyance as ordinarily understood, i.e., the power of seeing at a distance, but rather the faculty of spiritual intuition, through which direct and certain knowledge is obtainable. This faculty is intimately connected with the "third eye," which mythological tradition ascribes to certain races of men." —Blavatsky, The Secret Doctrine
"This opened eye is the purely spiritual sight of the adept. However, it is necessary to clarify that this is not clairvoyance, but rather the faculty of spiritual intuition, through which direct and true knowledge can be acquired." —Samael Aun Weor, Cosmic Teachings of a Lama