The BFSS matrix model (Banks-Fischler-Shenker-Susskind 96) is the description of the worldline dynamics of interacting D0-branes. In the limit of large number of D0 branes supposed to encode the strong coupling limit of type IIA string theory (see also at M-theory).
The BFSS matrix model was argued to arise in several equivalent ways: as the worldvolume theory of a large number of D0-branes in type IIA, as the KK-compactification of 10 SYM to zero space dimensions, or as a certain non-commutative limit of of the worldsheet action of the M2-brane in M-theory. 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 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 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).
The original article is
Further perspective includes
A review of further developments is in
Relation to the 6d (2,0)-supersymmetric QFT: