Try MapAt.
test = Partition[Range[8], 2]
(*{{1, 2}, {3, 4}, {5, 6}, {7, 8}}*)
MapAt[f, test, {All, 1}] (*apply to first column*)
(*{{f[1], 2}, {f[3], 4}, {f[5], 6}, {f[7], 8}}*)
MapAt[f, test, {2 ;; ;; 2}] (*apply to every other starting at position 2*)
(*{{1, 2}, f[{3, 4}], {5, 6}, f[{7, 8}]}*)
MapAt[f, test, {3, 1}] (*apply to specific location*)
(*{{1, 2}, {3, 4}, {f[5], 6}, {7, 8}}*)
So, since you want Abs applied to the second column:
m = {{1, -1}, {-2, 2}, {3, -3}};
MapAt[Abs, m, {All, 2}]
(*{{1, 1}, {-2, 2}, {3, 3}}*)