Souls are conscious forms of life that exist within all, from plants, to animals, and more sophisticated creatures, such as humans. The soul generates mana for the body to use. For more information, see anatomy.
The soul is a ethereal entity. In a sense, it's 'static', meaning if the soul is injured in anyway, it will not be able to be repaired, at least not through natural means. Often referred to as one's spirit, the soul is also viewed as the mind's consciousness. This view is significantly popular, as most, if not all, emotions are tethered to the soul. The idea of 'right' and 'wrong' is also closely associated with one's spirit, as such the soul can be seen as the physical representations of the body's emotion.
Make no mistake, this does not mean that the soul functions as the brain. While the soul is indeed needed to experience the aforementioned sensations, the brain is what allows the body-- and soul through extension-- to analyze and actually understand information being presented within the world.
As a direct result of being unable to repair oneself through natural means, the use of Divine magic often leads to early deaths for its wielders. This speaks in reference to the souls that mortals possess.
If Reincarnation Occurs, the soul is cleansed and renewed in a new body, the memories from the previous life are still there, but are rarely found
An Angel's soul follows many of the principles of a mortal's. However, there are glaring differences.
The most important difference being that an Angel's soul can actually repair itself overtime. As such, killing an angel isn't realistically possible as they'd simply return if given enough time. Alongside this, as a result of this property, Angels are able to freely utilize Divine Magic, which utilizes the soul at it's core in order to perform magical abilities. While it will deteriorate the user's soul as it would anyone else, the Angel would be able to rejuvenate their spirit, as if he/she were merely using an everyday mana technique.
Like the soul of a mortal, an Angel's spirit also represents their mind's consciousness. Yet the difference lies in how said consciousness function. From the beginning, their souls are pure, unable to possess any malevolent emotions or thoughts. That is, however, until the Angel happens upon corruption or depravity. Once this occurs, the negative emotions floods through, pretty much infecting the soul indefinitely, and thus creating Fallen Angels. At this stage, the soul has entered the point of no return and will never be 'pure' again.
One interesting property of this ethereal entity is the fact that an Angel's soul can legitimately be viewed through their wings. As a result, it's quite easily possible to see whether one has fallen or not.