Soul
A soul s the immortal essence of a person. Ideally, it re-enters the reincarnation cycle upon death.
Characteristics
A souls is highly malleable, but embodies a few core qualities that set it apart from the rest. For example, while Mizar's personality might fluctuate wildly from reincarnation to reincarnation due to the circumstances, whomever bears it will almost always be full of life, colour, and energy.
Reincarnation
Before being reincarnated, souls enter an 'in between' phase. In this state, they are a vague mix of all they previous past lives. Ordinarily, they feel a sense of peace and love, being intently connected to all who ever might have cared about them in a way that would never have been possible in the world of the living. In this state, it is possible for a being of higer power (such as Alcor) separate the soul from the others, and draw forth the persona of a specific life, bringing it to the forefront- though it takes a great deal of energy to do so.
A soul can be
Certain souls, have particular instinctual 'preferences' when it comes to whom they will be reincarnated as, such as gender (more often than not, Mizar is reincarnated female).