I can wrap my head around using a 2D Perlin noise function to generate the height value, but I don't understand why a 3D Perlin noise function would be used.
In Notch's blog, he mentioned using a 3D Perlin noise function for the terrain generation on Minecraft. How would that be done and why would it be useful? If you are passing x, y, and z values, doesn't that imply you already have the height?
Well, Minecraft is about mines. Notch tried to solve: "How do I get holes / overhangs in my world?"
Since 2D Perlin noise generates nice/smooth looking hills, 3D Perlin noise will generate nice/smooth hills and nice holes in your 3D voxel grid.
An implementation can be found here (while that is an n-dimensional solution).
In other use cases the Z component of a 3D Perlin noise is set to the current time. This way you will get a smooth transition between different 2D Perlin noises and that can be used as groundwork for fluid textures.