Rebirth is the process by which a soul enters the developing body of an unborn child and begins a new life. Usually they aren't capable of determining their sex or race, although personal preference and identity is believed to play at least some part in it. Some people are consistently born as one particular sex or species, while others vary wildly.
Typically, the new being has the same Talents as the old one, but they have been known to change and shift over the rebirth process. Sometimes they grow weaker or stronger, while other times a person may gain or lose entire Talents. But as a general rule, Talents tend to remain relatively consistent.
The personality of the new person can be very different, depending upon their experiences, although it will typically have a similar rooting. People are rarely surprised to learn what their other selves did.
Memory does not always remain constant during rebirth. Under normal circumstances, the infant will not remember their past lives at all. Mage children may sometimes slowly recover their memories, bit by bit, through dreams and flashbacks, until adulthood, especially if the child is inborn to Mind Magic or used memory mnemonics in their previous life to assist in recall. If they reach adulthood without fully recovering their memories, chances are they will not recover them on their own, and will need the assistance of memory magic. Mind Magic alone is capable of restoring memories to some extent, but to recover ones that have been completely lost, Time Magic is needed as well.