Plane
The term plane is a tricky one. It is roughly synonymous with the term universe, though plane has more esoteric connotations. Colloquially, the word dimension is sometimes used to refer to the same idea, but I use dimension exclusively to refer to the three dimensions of space and one dimension of time.
A plane can be understood as a "region" of reality with its own physical properties. Physically, planes are inaccessible or nigh-inaccessible from other planes. Baator and Celestia are examples of planes.
The nature of the planes which make up the known multiverse is a hotly debated topic. There are several major cosmological theories which aim to explain the structure of the multiverse. The most widely accepted one is the Great Wheel. Others include the World Tree and World Axis.
Furthermore, cosmological models regarding the material planes abound. One major one is the Prime Material model, which states that there really is only one material plane, and every "world" (Greyhawk, Eberron, the Forgotten Realms, etc.) is physically accessible from another; you can literally get into a rocket ship and fly from Oerth to Toril. Each star system is encased inside of a crystal sphere, and these crystal spheres float in a vast, outer space–like ocean of phlogiston.
Another theory (note: this is the one that's true in Marillia), is that there are many material planes (one in which Greyhawk exists, one in which Eberron exists, etc.), and they exist in parallel to each other: they're parallel material universes.
Properties
Not all planes have the same properties. For example, Baator is notorious for having highly warped spatial dimensions; e.g., going from point A to point B might take 10 minutes, but going from point B back to point A might take 6 hours. Many planes also have a warped temporal dimension; e.g., Ludecco spent several weeks in Celestia, and it was equivalent to just a couple of hours in Marillia.
See also
Gallery
The Prime Material
