In programming I've come across the idea of arrays containing arrays containing arrays etc., and as it's pretty intuitive to think of an array of arrays as a matrix, it seems like a reasonable idea to think of higher structures as higher-dimensional matrices. Unfortunately, trying to find out about n-dimensional matrices is difficult, as searching for '3d' gives $3\times3$ matrices, and any other reference to dimension gives rise to information concerning the height and width of a regular matrix.

So are higher-dimensional matrices used in maths for anything in particular? I'm assuming they might have some links to mathematical physics, or some kind of modelling where there are many constraints/equations in a system. Even if not, could somebody provide some links to where I can read a bit more about the idea, or (if possible) give me some interesting ideas, theorems, proofs, applications about them? I am more interested in the pure side of things rather than simply lists of how they might be used, but any information would be lovely. Thanks in advance!