Plane

Put simply, a plane is a reality whose boundaries can only be pierced by a Planeswalker or other similar entities. There are almost infinite planes in the Omniverse, separated by the void known as the Blind Eternities (a chaotic maelstrom of mana and aether).

Their size is itself limitless, as some planes are only a single universe, where as others are entire megaverses. Most known planes have one central, populated world, that the entire plane is typically named after*. However, in more vast planes with billions of galaxies and stars other populated worlds can also exist - as well as the less frequent case of multi-dimensional planes.
The inhabitants of most planes have no idea that theirs is not the only reality, — generally only Planeswalkers know that, and they typically do not share this fact. These non-Planeswalkers which comprise the vast majority of life in the Omniverse are called planebound.
Planes are usually fairly different from each other, and only traversable by Planeswalkers. However, they cannot planeswalk between realities that are too similar - i.e. timelines. While too similar for Planeswalkers to be able to easily jump between, there are many planes home to at least one planebound being called a Timewalker who can easily jump between the timelines and is often able to ferry others along with them.


*Near-Earths do not follow this convention.

Worldsouls

All planes have a Worldsoul, a central consciousness (for lack of a better term) that is at the heart of the plane. For planes with many planets, it usually rests on the most populated or important one but there are exceptions to this such as in the Lucorusant Megaverse where the Worldsoul is omnipresent throughout the plane.
These consciousnesses will often act in defense of the plane when it is threatened, and will manifest via avatars. The avatars are typically gargantuan magical beings that embody the plane, but they can be dispelled via magical or physical means with no damage to the plane's stability.
They are also known to be able to communicate with certain individuals who are very in tune with the plane itself. These individuals are typically able to command the avatars in a limited fashion, and can also bend the leylines of the planes temporarily to aid them.
When a plane is destroyed, the Worldsoul persists and will be adrift in the Blind Eternities. In extremely rare cases they then might settle on the surface of another plane and exist as an Entity. These Entities will seep into an area and attempt to recoup power, but will be unable to obtain any significant power to supplant the Worldsoul of the plane they are on (for it would destroy them if they tried). In two of the handful of known cases, when the Entities realized this fact, they attached themselves to a planebound individual - making those people into Planeswalkers. Due to the limited sample size, it is unknown if these individuals would cease planeswalking should their Entity leave them.