Listable is an attribute that can be assigned to a symbol f to indicate that the function f should automatically be threaded over lists that appear as its arguments.
Listable functions are effectively applied separately to each element in a list, or to corresponding elements in each list if there is more than one list.
Most built-in mathematical functions are Listable.
Example: Log is Listable. Log[a,b,c] .
All the arguments which are lists in a Listable function must be of the same length.
Arguments that are not lists are copied as many times as there are elements in the lists.
Example: Plus is Listable. a, b, c + x .
See The Mathematica Book: Section 2.5.3.
See also: Thread, Map, Sequence.