Comprehensions are a concise notation, both perform some operation for a collection of elements, and/or select a subset of them that meet some condition. They are borrowed from the functional programming language Haskell (https://www.haskell.org/), and contribute to giving Python a functional flavor, together with iterators and generators.

Python offers you different types of comprehensions: list, dict, and set. We'll concentrate on the first one for now, and then it will be easy to explain the other two.

Let's start with a very simple example. I want to calculate a list with the squares of the first 10 natural numbers. How would you do it? There are a couple of equivalent ways:

# squares.map.py
# If you code like this you are not a Python dev! ;)
>>> squares = []
>>> for n in range(10):
...     squares.append(n ** 2)
...
>>> squares
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

# This is better, one line, nice and readable
>>> squares = map(lambda n: n**2, range(10))
>>> _(squares)
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

The preceding example should be nothing new for you. Let's see how to achieve the same result using a list comprehension:

# squares.comprehension.py
>>> [n ** 2 for n in range(10)]
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

As simple as that. Isn't it elegant? Basically we have put a for loop within square brackets. Let's now filter out the odd squares. I'll show you how to do it with map and filter first, and then using a list comprehension again:

# even.squares.py
# using map and filter
sq1 = list(
    map(lambda n: n ** 2, filter(lambda n: not n % 2, range(10)))
)
# equivalent, but using list comprehensions
sq2 = [n ** 2 for n in range(10) if not n % 2]

print(sq1, sq1 == sq2)  # prints: [0, 4, 16, 36, 64] True

I think that now the difference in readability is evident. The list comprehension reads much better. It's almost English: give me all squares (n ** 2) for n between 0 and 9 if n is even.

According to the Python documentation: