Spirit Realm

The spirit realm is the dimension where spiritual beings reside. It exists parallel to the material realm as the realm of the unseen. In essence, it is an extra "layer" or dimension to the world, distinct from the material realm yet no more separable from it than space is from time.
The spirit realm is, at its core, the realm of vitality. Vitality is the life essence which all living beings have, but it is also what spirits are made of. It is those spirits—vitality not bound to a physical form—which make up the spirit realm.
Spirits of the dead (also known as ghosts) can be found in the spirit realm. There is no consensus on whether there are other types of spirits as well or if all spirits are ghosts. Some say there are divine and/or demonic entities in the spirit realm, but again this is a matter of interpretation and belief.

Spirits in the Material World

(Technically, it's the material realm, but, you know.)
The boundary between the spirit and material realms is not absolute, and it is possible for spirits to manifest in the material realm. Usually, they appear as apparitions, but there have been cases of spirits being able to physically interact with objects or living beings.

Living Beings and the Spirit Realm

It is possible for humans and other living beings to interact with or even cross over into the spirit realm. This requires one to be able to perceive vitality, an ability which can be innate or learned. (This is a necessary skill for shamans, who serve as the intermediaries between the material and spirit realms, but it is possible for non-shamans to enter the spirit realm.)
At the most basic level, this involves attuning oneself to the spirit realm, allowing both realms to be perceived at once. Spirits generally appear apparitional at this level but can be spoken with.
Deeper immersion—actually crossing over into the spirit world—involves entering a trance state and temporarily abandoning one's physical body. Inside the spirit realm, spirits are wholly real, while living things are apparitional or nonexistent and cannot be interacted with. Nonliving things, especially manmade things, also become apparitional or nonexistant.
The deeper one manages to immerse oneself in the spirit realm, the less it reflects the living world and the more it seems purely a world of the spirits. Theoretically, if someone fully detached themself from the material realm, everything but the spirits themselves would become imperceptible to them, but no living person has experienced this. Even spirits invariably seem to have some level of awareness of the material.

Mana and the Spirit Realm

Mana is not bound to one side of the divide between the material and the spiritual. Like time and space, mana is the same on either side. Sprites, which consist purely of mana, exist in both the material and spirit realms simultaneously. Perhaps this is why magic can be used to summon spirits or be used by spirits to physically manifest.

Type

Dimensional plane