The word non-duality is English translation of Sanskrit word "Advaita", which means not two or non-dual. This word is an effort to put the condition and position of God or Consciousness and our experience of world in human language. We now look at the significance of this word in detail.
When ancient seers came to conclusion through reasoning and experience that there is only one homogeneous Consciousness which we experience in different states of waking, dreaming and deep sleep, they found it very difficult to define it's exact nature. The problem was, they could not call it one since one inherently brings the idea of two or more possibilities. Plus the word "one" gives idea of loneliness, God or Consciousness is not lonely. At the same time there is nothing other existing in reality. So to bring the status of God into human language they called it Advaita, non-dual, which means there is neither one nor many but something which cannot be defined in language.