Map

Map(f, expr)  or  f /@ expr

applies f to each part on the first level of expr.

Map(f, expr, levelspec)

applies f to each level specified by levelspec of expr.

>> f /@ {1, 2, 3}
{f(1),f(2),f(3)}
>> #^2& /@ {1, 2, 3, 4}
{1,4,9,16}

Map f on the second level:

>> Map(f, {{a, b}, {c, d, e}}, {2})
{{f(a),f(b)},{f(c),f(d),f(e)}}

Include heads:

>> Map(f, a + b + c, Heads->True)
f(Plus)[f(a),f(b),f(c)]

Level specification a + b is not of the form n, {n}, or {m, n}.

>> Map(f, expr, a+b, Heads->True)
Map(f, expr, a + b, Heads -> True)