World Mechanics - Realms

Dimension (Realm, World)

A plane of existence
Each plane is given an arbitrary number, generally given in order of discovery. Exceptions to this are the third and 0th realm, the third realm being named after the number of perceived dimensions in the world, the 0th realm is named such because it is thought to be the origin of all realms.
Magic occurs when another realm is accessed. In the third realm, magicians reach out to other realms to cast magic; when they do so, they temporarily overwrite nature and physics of the third realm with the realm of another world.

A majority of magic is drawn from the 0th realm.

To put it simply, a world is just a parallel dimension. There are infinite parallel dimensions of an infinite amount of permutations in stOP, and each dimension is self-contained. For the most part, at least.
In the case of Earth, or the 3rd realm, it is possible to access other dimensions, albeit briefly. Doing this allows somebody to bring some power from another realm. Essentially, this allows a person to superimpose a reality that isn't Earth into Earth. Some worlds conform to different physics, where things such as casting fire or speaking to animals are commonplace.
A magician is a person who can access this world, bring its reality to Earth temporarily, and then control that reality to cast some sort of magic. For Earth, most magic is drawn from the 0th realm, as it is the easiest to access and the most malleable of the realms.
Back to dimensions... dimensions are not strictly 'parallel worlds' or 'parallel earths.' It is easier to think of each dimension as a collection of rules that form a world or a universe. For instance, there can be realms that exist that are only one dimensional, or realms that are completely dimensionless, or realms that are composed entirely of other realms.
These realms also need not have any semblance to Earth's realm. It is possible there exists a realm where organisms live in space, and living on a planet is seen as impossible. There can be a realm where time runs backwards, or a realm where color doesn't exist. There's really no limit to what a realm can be, although within the scope of most stories in stOP, a realm will be an Earth-like world with properties that aren't Earth-like.