Souls are important! Most living things have them.
Although the soul doesn't have to be in one piece, soul fragmenting is where you break a soul into multiple pieces, each piece can have a will of its own and usual contributes to a greater more whole soul, usually the soul fragments have personality disorders or other issues. soul fragments are completely isolated from each other.
In addition multiple souls can be linked together this will lead to effects on the soul being felt for all souls connected. for example enchantments.
Finally souls can be duplicated, although this kind of thing is extremely difficult to achieved for a regular or even advanced magic user, usually achieved by non-human magical creatures as will lead to a perfect copy of the soul, although if done wrong can lead to soul fragmenting.