If we regard M as defining a map of graded right free modules, then M_n returns the induced map of underlying R-modules in degree n, where R is the coefficient ring of ring M.
The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NCAlgebra/NCAlgebraDoc.m2:4284:0.