The significance of the Nataraja sculpture is said to be that Shiva is shown as the source of all movement within the cosmos, represented by the arch of flames. The purpose of the dance is to release men from illusion of the idea of the "self" and of the physical world.
In recent years the term nonduality has steadily crept into the vocabulary of many Western spiritual teachings, but there is often some lack of common understanding as to just what is represented by nonduality. It is generally accepted that nonduality is a translation of the sanskrit term Advaita, which literally translates as "not two," and is utilized in the naming of the ancient Indian wisdom tradition called Advaita Vedanta. In the modern vernacular, nondual (or non-dual) is a word intended to point to the fact that reality is only one thing - one single reality manifesting in appearance as more than one, but fundamentally there is only the one. One might even say there is only God (or whatever term you might prefer such as Being, Universe, Truth, Life, etc.) and that is not distinct from who you are. It's another way of saying there is only oneness. This is different from saying everything is interconnected, because with interconnectedness there are various things (more than one thing, thus dual) that are connected to each other. Nonduality points toward there being no separate objects, thoughts, emotions, sensations or even universe. It is all one grand appearance, and it appears to flow in time.
Nondual spiritual teachings are based on the idea that duality, or separation, is only one perspective of the totality of reality, and belief in our separateness forms the basis for most of the difficulties and suffering we encounter personally and globally. Nondual teachings are intended to point toward recognizing an additional perspective of unity, or oneness, different from the ordinary view we learned as children through our collective conditioning. The process leading to directly recognizing and experiencing nonduality often seems to require personal inquiry into the truth of many of our long-standing thought habits, beliefs and concepts. Such inquiry often takes the form of questions such as "Who Am I" or "What Am I" that in turn lead to exploring what is the nature of self, and do I really have a separate independent existence?
Albert Einstein once said "A human being is part of a whole, called by us the Universe, a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest - a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison." These are words reflecting nonduality.
The first line of the Tao Te Ching by Lao-tzu states "The tao that can be told is not the eternal Tao." So, too, the nonduality that can be described or written is not the direct knowing of nonduality. It's like the taste of chocolate cannot be expressed in words but must be experienced directly. Nevertheless, writers continue to offer their understandings for the benefit of humanity. Here are some links you can follow to a few of these offerings.