The following is from the book "Kabbalah and Meditations for the Nations" by Rabbi Yitzchak Ginsburgh .
The nature of the soul
In order to understand why God gave these seven specific commandments – the Laws of Bnei Noach – to all humanity, we must first briefly explain how the human soul functions.
The human soul has both a Divine and a physical, or animal aspect. In Hebrew these are referred to as the Divine soul (nefesh Elokit) and the animal soul (nefesh behamit) as defined in the Tanya, by the Chassidic Master, Rabbi Shneur Zalman of Liadi. All human beings posses a Divine spark. The difference between one human and another lies in the extent to which the spark has entered and plays an active role in his or her psyche. (We use the term “physche” to refer to both the conscious and unconscious planes of the soul).
When the spark fully enters the psyche it is known as a Divine soul. And so we speak of Jews as possessing a Divine soul. With regard to a non-Jew, the Divine spark hovers above the psyche (not entering it even on the unconscious plane). A righteous gentile (that is, a non-Jew who fulfils the seven laws of Bnei Noach) is one who senses the presence of the Divine spark and is inspired by it to walk along the path of God fitting for all people as outlined in the Torah. On the other hand, a non-Jew who has not yet become a righteous gentile is unaware of the Divine spark hovering above.
To use the language of Chassidut, the Divine spark (or soul) of a Jew is considered an inner light (or pnimi), meaning that it is directly experienced and makes for part of his or her psychological makeup. The righteous gentile’s non Jew’s spark of Divinity is described as a “closely surrounding light” (or makif karov), meaning that it is psychologically experienced only indirectly. The Divine spark of a non-Jews who are not considered righteous gentiles is akin to a “distantly surrounding light” (or makif rachok), meaning that it plays no conscious role in that person’s experience as a human being.
Even in this third case, due to the refinement of character that results from life’s trials and tribulations, and due to the Divinely ordained meetings between non-Jews and Jews which introduce the beauty of the Torah to the non-Jew, the “distant” spark may grow “closer” and the “close” spark may even desire to convert to Judaism. It is because of this latent potential innate in every non-Jew that we speak of all non-Jews as possessing a Divine spark. Indeed all of God’s creations are continuously brought into being by means of a Divine spark, but, only a human being, even if born a non-Jew, is able to convert in his present lifetime and become a Jew.
(Kabbalah and Meditations of the Nations, Chapter 3 “The Mystical Symbolism of the Seven Laws of Bnei Noach, pg 55-56)