Matrix division means multiplying one matrix by the inverse of another matrix. Matrix A "divided by" matrix B is equivalent to matrix A multiplied by the inverse of matrix B. Mathematicians usually use the term "multiplying by the inverse" rather than "dividing" when working with matrices.
The inverse of a matrix A is the matrix that can be multiplied by A to give the identity matrix, in which all diagonal elements are equal to 1 and all other elements equal 0. Some matrices do not have an inverse; these are called singular matrices. One cannot divide by a singular matrix.