What are the uses of multi-dimensional arrays?
One could just as easily ask "what are the uses of multidimensional spaces?"  After all, with space-filling curves, all we really need is one dimension.

But a single dimension, even if it's sufficient, does not always yield useful models.  For example, a 2-dimensional euclidean line would be non-continuous when mapped to a space-filling curve.

It's the same with multi-dimensional arrays -- they're used not because they're inherently necessary, but because they're a useful model.

For example, let's take a look at how one might model a movie.


A movie is nothing more than a time-varying sequence of images -- i.e., an array of images.
Each image is a two-dimensional array, with each element of the array representing a color.
A color has three components:


Red
Green
Blue



So a movie can be modeled as a multidimensional array.