The death barrier or death plane is a special type of floor that causes Mario to lose a life if he is above it and vertically within 2048 units of it. It is analogous to the bottomless pits of previous games. A floor is used for this case since Mario cannot inhabit any region without a floor triangle underneath him, as that is considered Out of Bounds.
The death animation triggers well above the physical height of a Death Barrier in order to avoid having Mario stand on it. However, it can be downwarped to or stood upon during a Power Star cutscene, and Mario's shadow is still visible on the surface of the Death Barrier, as with any other floor. The death barrier can also be reached by flying downwards using the Wing Cap with a lot of speed (doable without hacks in TotWC and WMotR).
Several objects, such as Goombas and Scuttlebugs, have special programming in place to despawn them if they reach the death barrier, to prevent them from walking around on top of it. The Mystery Goomba only exists for one frame, as it spawns at the death barrier and consequently despawns as soon as possible, and at the same time is too far away from Mario to be able to load.