Apply[Plus, {{a, b, c}, {d, e, f}, {g, h, i}}]
same as
Plus @@ {{a, b, c}, {d, e, f}, {g, h, i}}
There are always many ways to do things in Mathematica...
MapThread[Plus, {{a, b, c}, {d, e, f}, {g, h, i}}]
Plus @@@ Transpose[{{a, b, c}, {d, e, f}, {g, h, i}}]