map doesn't relate to a Cartesian product at all, although I imagine someone well versed in functional programming could come up with some impossible to understand way of generating a one using map.

map in Python 3 is equivalent to this:

def map(func, iterable):
    for i in iterable:
        yield func(i)

and the only difference in Python 2 is that it will build up a full list of results to return all at once instead of yielding.

Although Python convention usually prefers list comprehensions (or generator expressions) to achieve the same result as a call to map, particularly if you're using a lambda expression as the first argument:

[func(i) for i in iterable]

As an example of what you asked for in the comments on the question - "turn a string into an array", by 'array' you probably want either a tuple or a list (both of them behave a little like arrays from other languages) -

 >>> a = "hello, world"
 >>> list(a)
['h', 'e', 'l', 'l', 'o', ',', ' ', 'w', 'o', 'r', 'l', 'd']
>>> tuple(a)
('h', 'e', 'l', 'l', 'o', ',', ' ', 'w', 'o', 'r', 'l', 'd')

A use of map here would be if you start with a list of strings instead of a single string - map can listify all of them individually:

>>> a = ["foo", "bar", "baz"]
>>> list(map(list, a))
[['f', 'o', 'o'], ['b', 'a', 'r'], ['b', 'a', 'z']]

Note that map(list, a) is equivalent in Python 2, but in Python 3 you need the list call if you want to do anything other than feed it into a for loop (or a processing function such as sum that only needs an iterable, and not a sequence). But also note again that a list comprehension is usually preferred:

>>> [list(b) for b in a]
[['f', 'o', 'o'], ['b', 'a', 'r'], ['b', 'a', 'z']]