S - the left-side of the assignment
ab(i,j:C)
means that columns j through C of row i will be updated with right-hand side of the assignment which is just
ab(i,j:C)-ab(i,j)/ab(j,j)*ab(j,j:C)
Is this code that you have written or obtained from somewhere? While it has some of the steps from gaussian elimination it seems to be incomplete.