The successor system is existence's own little way of keeping balance regarding Embodiments being killed, which has happened many times in the past, and will most likely continue to happen in the future.
"Named" successors - A name successor is a mortal, or pseudo-immortal who has been given the title as heir to a force or aspect of existence. When and if that Embodiment dies, or retires from their position, the named becomes the Embodiment through a ritual known as the Ascension.
"Unnamed" successors - A very rare occurrence, as mortals and pseudo-immortals are rarely born with a strong attraction or affinity for an aspect of existence strong enough to become an Embodiment this way. If a named and their Embodiment benefactor are killed, and there is a true unnamed in existence, they are flooded with the power, most die, but some become the Embodiment.
These are the only two natural ways to become an Embodiment, there are however very dangerous and forbidden magics that allow for a much less..natural transfer of power.
Descendent ritual - Embodiments sometime have children, or a bloodline that runs deep, very deep in the mortal world. Sometimes an embodiment can have thousands of descendants, as they live throughout time unchanging. This is the descendant ritual, an ancient and evil magic that allows for a descendant to steal the powers of their Embodiment ancestor. Therefore killing them and raising themselves to the grand position as a God. The details of the ritual have been lost to TIME.
Twin successor scenario - Very few aspects of existence can be divided into two avatars, two Embodiments for one force. In Destruction's case, he name his child successor while he was just being conceived. When the embryo split into twins, it split their share of the force. Causing a rift in the power of Destruction. They will never be the full successors, and the force will not have an Embodiment until one of them dies, or relinquishes their right to the power.
Just a few things about it, if you have anymore questions ask me.