According to many theological and philosophical traditions, a Soul is described as the self-aware, immortal essence of a living being. It is typically considered to be immaterial, possibly existing as some form of ethereal energy. Most religions, including Christianity, Judaism, Hinduism, Islam, and Buddhism, have some concept of the Soul, and most consider it to be the true source of human sentience. It is particularly prevalent in Christianity, where the Soul is believed to survive physical death, later to be judged by God.
The term is almost parallel to the commonly accepted and theologically-neutral concepts of the human mind or psyche, however while the mind is dependant on the proper functioning of the physical brain (to use an analogy, like computer software is dependant on computer hardware), the Soul is believed to be independent of the physical body and therefore immortal.
The existence of Souls, while long debated, has yet to be acknowledged by modern science. The term is generally considered to have mystical or religious connotations, and while often used poetically, is considered taboo in scientific circles. The concept has also been criticized as a form of escape or detachment from one's physical body. Organized religion has often carried the brunt of this criticism for what some consider to be it's capitalizing on the fears and suffering of the human condition by promising an afterlife.
Neon Genesis Evangelion makes repeated references to the concept of Souls. In fact the existence of Souls is not a theory but a proven scientific fact in the series, and Metaphysical Biology is a genuine scientific field of research in that area. Most references to the Soul involve the Evangelion Units, which as artificial constructs created by mankind, have no Souls of their own (in Christian theology only God may create or 'breathe' Souls into existence). Evangelion Unit-01 and Evangelion Unit-02 do however posses transplanted human Souls of Yui Ikari and Kyouko Zeppelin Sohryu respectively.
The term is also used several times in reference to the Dummy System. Ritsuko Akagi explains that while they have the ability to duplicate and mimic the personality and thought patterns of a human mind for the purposes of the Dummy Plugs or the MAGI Super-Computer System, they cannot digitalize the Soul, thus making a distinction between the two concepts.
In the series every human is believed to posses a Soul, which is a requirement for the projection of an AT Field (consequently the Angels also posses Souls). In The End of Evangelion, as Lilith breaks down all the AT Fields on the planet, human Souls (depicted as bright red lights) are drawn back into the Black Moon as part of the Human Instrumentality Project.