Whatever exists is one: the ultimate Reality called Brahman. But Brahman appears as the universe of names and forms because of maya, the veiling and projecting power inherent in it. At twilight, we can mistake a rope for a snake and experience fear and trepidation by seeing the "snake." If we shine a flashlight on the "snake," we see the rope as it is. The snake never actually appeared or disappeared. Similarly, in the darkness of ignorance of the Divine in us, we perceive the universe in place of Brahman; but in the light of Self-knowledge, assures Vedanta, the universe will "disappear" and Brahman will reveal itself.
Similarly, our body and mind are appearances on the Atman, our true spiritual Self and the source of eternal Bliss. Yet due to our attachment to our body and mind, we look for lasting fulfillment in the outside world. When wisdom awakens in us, we understand that the world cannot bring us either peace or fulfillment.
So all beings and things in the universe are just one existence appearing as many. This truth of oneness of existence has several practical implications.
Change of attitude toward others
When we look upon ourselves as Spirit, we naturally look upon others as the same Spirit. We give up judging people by their physical or mental differences, and strive hard to perfect ourselves, so that we will always see oneness around us. A spontaneous sequel to this attitude is looking upon all forms of service as worship of the Divine in others. And our love for others will not stop at the human level, but extend to all living beings.
Growing in unselfishness
Practice of the truth of oneness will help us reduce our selfishness and grow in unselfishness. After exhorting us to cultivate faith in ourselves, Swami Vivekananda explains: "But it is not selfish faith because Vedanta, again, is the doctrine of oneness. It means faith in all, because you are all. Love for yourself means love for all-love for animals, love for everything; for you are all."
Looking upon everyone as Spirit does not prevent us from seeking holy company in preference to bad company. Divinity is the core in everyone, but it manifests in different degrees in different people. While seeking holy company, however, we should take care not to hate people or judge them as bad.
Loving and serving others as manifestations of Spirit fosters in us equanimity and detachment. The universal love advocated by Vedanta is based on the truth of oneness of existence: "Verily, not for the sake of the husband is the husband loved, but he is loved for the sake of the self [which, in its true nature, is one with the Supreme Self]. Verily, not for the sake of the wife is the wife loved, but she is loved for the sake of the self....Verily, not for the sake of the All is the All loved, but it is loved for the sake of the self. Verily, it is the Self that should be realized-should be heard of, reflected on, and meditated upon." (Brihadaranyaka Upanishad, 2.4.5)
The saying, "Love thy neighbor as thyself" makes good sense since our neighbor is truly ourself.