The Spirit World is a dimension/plane prominently featured in the episode "Beyond this Earthly Realm" from Season 4. It seems to overlap the physical world for the most part, but functions differently. While spirits in the Spirit World cannot touch beings in the physical world, they can touch the walls and influence materials and electricity.
In Beyond this Earthly Realm, Finn enters the Spirit World by touching the lamb relic, making it so that beings in the physical world cannot see him. The exception to this (at least in the episode) was the Ice King, who was able to see Finn thanks to his Wizard Eyes. Whether that means others can learn to see spirits or not is unknown. The Ice King also said that there are portals all around the universe, it is unknown if it is connected to other dimensions.
There are many entrances to it, and some of these seem to create portals between one another as the hole in the Ice Kingdom that functioned as an entrance led back to the Mystery Cave with the porcelain lamb. This suggests that while the Spirit World overlaps the physical world, it treats space differently or can link two points with portals.
It is likely that the Spirit World was featured in "Mortal Recoil" also as it gives us the Ice King's perspective through his Wizard Eyes. However, at that point it was suggested that the hallucinations he sees are fake.