Soul is a dark, inorganic mass that glows with the azure (blue and green) light. It is a person's true form. Rather than something intangible, it is more of an actual object.
Souls are often used as a catalyst for the Cauldrons and Nox Nyctores. They were also used in creation of the Embryo, the new Azure and the true BlazBlue, at the end of BlazBlue: Chronophantasma. After the life of the soul's owner ends, it returns to the Azure, where it is stored and preserved along with all the information it possess.
Powerful souls tend to manifest a special ability called a Drive. A strong soul is also capable of protecting it's owner from the effects of the Boundary, as seen in the cases of Relius Clover, Jin Kisaragi and Makoto Nanaya, that had ventured through it, as well as time and space, relatively safely. Because they show the true form of someone, even basic information like the person's sex is clear to those who can see the souls form – as in the case of Relius easily determining Mai Natsume's original gender within seconds of meeting her.
One of the Detonator's basic components is a powerful soul. Relius pondered whether the souls of Jin and Makoto would have been a good material for it. In Makoto's bad ending, after Relius gets his hands on her soul, he claims that she is a far better material for the Detonator than Ada was.
Another type of special souls, are those possessed by the ones with the power to control the flow of life, as only those types of souls can be used as key-power source for the Kushinada's Lynchpin.
Hakumen's own soul is very different from a standard one. When Arakune first saw it, he was baffled at the fact that something that should be high in the skies, was here on earth, right before him. He compared it to a white dwarf star.