In computational chemistry, we create basis sets, which, to my understanding, are basically matrices of functions that are used to describe the wavefunction of the system. Is this true?

Sort of – I do no know what a “matrices of functions” means exactly. Basis sets are groups of functions called eigenfunctions. Any function within the Hilbert spanned by this basis can be represented by a linear combination of eigenfunctions.

where N is the number of functions in the basis, and the \vec{r}_M represent a discrete spatial mesh consisting of M points. (One could cover all of space by replacing the mesh with a continuous variable, but that formally takes a bit of care.)