Improving Map Function on Lists

{n, m} = {10^4, 10^4};
offset = RandomReal[1, n];

data = RandomReal[1, {m, n}];

cf = Compile[{{v, _Real, 1}, {offset, _Real, 1}}, 
   Table[v[[i]] - offset[[i]], {i, Length[v]}],
   RuntimeAttributes -> {Listable}, CompilationTarget -> "C", 
   RuntimeOptions -> "Speed"];

r1 = (# - offset) & /@ data; // RepeatedTiming
r2 = Plus[data, ConstantArray[-offset, m]]; // RepeatedTiming
r3 = ArrayReshape[Outer[Plus, Developer`ToPackedArray@{-offset}, data, 1], 
      {m, n}]; // RepeatedTiming
r4 = cf[data, offset]; // RepeatedTiming

r1 == r2 == r3 == r4

Output

{1.08, Null}

{0.557, Null}

{0.233, Null}

{0.20, Null}

True

A slightly faster method uses KroneckerProduct to create a suitable matrix of offsets. Some data:

{n, m} = {10^4, 10^4};
offset = RandomReal[100, n];
data = RandomReal[100, {m, n}];

Your method:

r1 = (#-offset)& /@ data; //AbsoluteTiming

{1.80568, Null}

Using KroneckerProduct:

r2 = data + KroneckerProduct[ConstantArray[-1., m], offset]; //AbsoluteTiming

{0.830738, Null}

Check:

r1 == r2

True

The Map version looks efficient compared with MapThread.

data2 = Flatten[ConstantArray[data, 100000], 1];
First[Timing[data3 = (# - offset) & /@ data2;]]

0.384383

First[Timing[
  data4 = MapThread[
     Plus, {data2, -ConstantArray[offset, Length[data2]]}];]]

2.80672

data3 == data4

True