Python for-in loop preceded by a variable

The current answers are good, but do not talk about how they are just syntactic sugar to some pattern that we are so used to.

Let's start with an example, say we have 10 numbers, and we want a subset of those that are greater than, say, 5.

>>> numbers = [12, 34, 1, 4, 4, 67, 37, 9, 0, 81]

For the above task, the below approaches below are totally identical to one another, and go from most verbose to concise, readable and pythonic:

Approach 1

result = []
for index in range(len(numbers)):
    if numbers[index] > 5:
        result.append(numbers[index])
print result  #Prints [12, 34, 67, 37, 9, 81]

Approach 2 (Slightly cleaner, for-in loops)

result = []
for number in numbers:
    if number > 5:
        result.append(number)
print result  #Prints [12, 34, 67, 37, 9, 81]

Approach 3 (Enter List Comprehension)

result = [number for number in numbers if number > 5]

or more generally:

[function(number) for number in numbers if condition(number)]

where:

function(x) takes an x and transforms it into something useful (like for instance: x*x)
if condition(x) returns any False-y value (False, None, empty string, empty list, etc ..) then the current iteration will be skipped (think continue). If the function return a non-False-y value then the current value makes it to the final resultant array (and goes through the transformation step above).

To understand the syntax in a slightly different manner, look at the Bonus section below.

For further information, follow the tutorial all other answers have linked: List Comprehension

Bonus

(Slightly un-pythonic, but putting it here for sake of completeness)

The example above can be written as:

result = filter(lambda x: x > 5, numbers)

The general expression above can be written as:

result = map(function, filter(condition, numbers)) #result is a list in Py2

It's a list comprehension

foo will be a filtered list of bar containing the objects with the attribute occupants > 1

bar can be a list, set, dict or any other iterable

Here is an example to clarify

>>> class Bar(object):
...   def __init__(self, occupants):
...     self.occupants = occupants
... 
>>> bar=[Bar(0), Bar(1), Bar(2), Bar(3)]
>>> foo = [x for x in bar if x.occupants > 1]
>>> foo
[<__main__.Bar object at 0xb748516c>, <__main__.Bar object at 0xb748518c>]

So foo has 2 Bar objects, but how do we check which ones they are? Lets add a __repr__ method to Bar so it is more informative

>>> Bar.__repr__=lambda self:"Bar(occupants={0})".format(self.occupants)
>>> foo
[Bar(occupants=2), Bar(occupants=3)]

Since the programming part of question is fully answered by others it is nice to know its relation to mathematics (set theory). Actually it is the Python implementation of Set builder notation:

Defining a set by axiom of specification:

B = { x є A : S(x) }

English translation: B is a set where its members are chosen from A, so B is a subset of A (B ⊂ A), where characteristic(s) specified by function S holds: S(x) == True

Defining B using list comprehension:

B = [x for x in A if S(x)]

So to build B with list comprehension, member(s) of B (denoted by x) are chosen from set A where S(x) == True (inclusion condition).

Note: Function S which returns a boolean is called predicate.