Duality/Dvaita is the I and Thou, a belief of separation between oneself and God (and others.)
Nonduality/Advaita is the Oneness of God/All divine energies and the manifest universe.
There is an interesting story told about this difference of beliefs. In India, sages like disputation with each other. Dattatreya*, an Avadhut and author of the Avadhuta Gita and the first guru to manifest in a body, was strolling through a town, when he came across such a disputation between those advocating Dvaita and those advocating Advaita. He listened to them for awhile, and then he told them, “If you are arguing about these differences, you still have a long way to go” [to enlightenment.]
Duality can be helpful in keeping our ego under control by recognizing that we are not omniscient, also having a place in one’s mind to direct our efforts and prayers.
Nonduality helps us to see the Creator and all Creation as one energy field. Thus, there is understanding that we are part of God and God vibrations are what we are made from. Reminds one of Genesis in the Bible saying that we are made in the image of God.
Nonduality in the heart is the understanding that there is no real separation between ourselves and others. We are all a part of the Divine Whole, and issues of culture and race and personality are seen in that context. Thus, the advanced person lives in Divine Love with all other creatures.
* You will find a whole chapter about Dattatreya and Guru in Ancient Power of Mantra and Ceremony, 3rd Ed., Volume I, Chapter 12.
Sadguru Dattatreya as the Male Trinity