In any case, it ends up being a quantum mechanical system whose degrees of freedom are a set of 9+1 large matrices. These play the role of would-be coordinate functions and their eigenvalues may be in interpreted as points in a spacetime thus defined.
In the 90s there was much excitement about the BFSS model, as people hoped it might provide a definition of M-theory. It is from these times that Edward Witten changed the original suggestion that “M” is for “magic, mystery and membrane” to the suggestion that it is for “magic, mystery and matrix”. (See Witten’s 2014 Kyoto prize speach, last paragraph).