What exactly are iterator, iterable, and iteration?

Iteration is a general term for taking each item of something, one after another. Any time you use a loop, explicit or implicit, to go over a group of items, that is iteration.

In Python, iterable and iterator have specific meanings.

An iterable is an object that has an __iter__ method which returns an iterator, or which defines a __getitem__ method that can take sequential indexes starting from zero (and raises an IndexError when the indexes are no longer valid). So an iterable is an object that you can get an iterator from.

An iterator is an object with a next (Python 2) or __next__ (Python 3) method.

Whenever you use a for loop, or map, or a list comprehension, etc. in Python, the next method is called automatically to get each item from the iterator, thus going through the process of iteration.

A good place to start learning would be the iterators section of the tutorial and the iterator types section of the standard types page. After you understand the basics, try the iterators section of the Functional Programming HOWTO.

Here's the explanation I use in teaching Python classes:

An ITERABLE is:

• anything that can be looped over (i.e. you can loop over a string or file) or
• anything that can appear on the right-side of a for-loop: for x in iterable: ... or
• anything you can call with iter() that will return an ITERATOR: iter(obj) or
• an object that defines __iter__ that returns a fresh ITERATOR, or it may have a __getitem__ method suitable for indexed lookup.

An ITERATOR is an object:

• with state that remembers where it is during iteration,
• with a __next__ method that:
  • returns the next value in the iteration
  • updates the state to point at the next value
  • signals when it is done by raising StopIteration
• and that is self-iterable (meaning that it has an __iter__ method that returns self).

Notes:

• The __next__ method in Python 3 is spelt next in Python 2, and
• The builtin function next() calls that method on the object passed to it.

For example:

>>> s = 'cat'      # s is an ITERABLE
                   # s is a str object that is immutable
                   # s has no state
                   # s has a __getitem__() method 

>>> t = iter(s)    # t is an ITERATOR
                   # t has state (it starts by pointing at the "c"
                   # t has a next() method and an __iter__() method

>>> next(t)        # the next() function returns the next value and advances the state
'c'
>>> next(t)        # the next() function returns the next value and advances
'a'
>>> next(t)        # the next() function returns the next value and advances
't'
>>> next(t)        # next() raises StopIteration to signal that iteration is complete
Traceback (most recent call last):
...
StopIteration

>>> iter(t) is t   # the iterator is self-iterable

The above answers are great, but as most of what I've seen, don't stress the distinction enough for people like me.

Also, people tend to get "too Pythonic" by putting definitions like "X is an object that has __foo__() method" before. Such definitions are correct--they are based on duck-typing philosophy, but the focus on methods tends to get between when trying to understand the concept in its simplicity.

So I add my version.

---

In natural language,

• iteration is the process of taking one element at a time in a row of elements.

In Python,

• iterable is an object that is, well, iterable, which simply put, means that it can be used in iteration, e.g. with a for loop. How? By using iterator. I'll explain below.

• ... while iterator is an object that defines how to actually do the iteration--specifically what is the next element. That's why it must have next() method.

Iterators are themselves also iterable, with the distinction that their __iter__() method returns the same object (self), regardless of whether or not its items have been consumed by previous calls to next().

---

So what does Python interpreter think when it sees for x in obj: statement?

Look, a for loop. Looks like a job for an iterator... Let's get one. ... There's this obj guy, so let's ask him.

"Mr. obj, do you have your iterator?" (... calls iter(obj), which calls obj.__iter__(), which happily hands out a shiny new iterator _i.)

OK, that was easy... Let's start iterating then. (x = _i.next() ... x = _i.next()...)

Since Mr. obj succeeded in this test (by having certain method returning a valid iterator), we reward him with adjective: you can now call him "iterable Mr. obj".

However, in simple cases, you don't normally benefit from having iterator and iterable separately. So you define only one object, which is also its own iterator. (Python does not really care that _i handed out by obj wasn't all that shiny, but just the obj itself.)

This is why in most examples I've seen (and what had been confusing me over and over), you can see:

class IterableExample(object):

    def __iter__(self):
        return self

    def next(self):
        pass

instead of

class Iterator(object):
    def next(self):
        pass

class Iterable(object):
    def __iter__(self):
        return Iterator()

There are cases, though, when you can benefit from having iterator separated from the iterable, such as when you want to have one row of items, but more "cursors". For example when you want to work with "current" and "forthcoming" elements, you can have separate iterators for both. Or multiple threads pulling from a huge list: each can have its own iterator to traverse over all items. See @Raymond's and @glglgl's answers above.

Imagine what you could do:

class SmartIterableExample(object):

    def create_iterator(self):
        # An amazingly powerful yet simple way to create arbitrary
        # iterator, utilizing object state (or not, if you are fan
        # of functional), magic and nuclear waste--no kittens hurt.
        pass    # don't forget to add the next() method

    def __iter__(self):
        return self.create_iterator()

Notes:

• I'll repeat again: iterator is not iterable. Iterator cannot be used as a "source" in for loop. What for loop primarily needs is __iter__() (that returns something with next()).

• Of course, for is not the only iteration loop, so above applies to some other constructs as well (while...).

• Iterator's next() can throw StopIteration to stop iteration. Does not have to, though, it can iterate forever or use other means.

• In the above "thought process", _i does not really exist. I've made up that name.

• There's a small change in Python 3.x: next() method (not the built-in) now must be called __next__(). Yes, it should have been like that all along.

• You can also think of it like this: iterable has the data, iterator pulls the next item

Disclaimer: I'm not a developer of any Python interpreter, so I don't really know what the interpreter "thinks". The musings above are solely demonstration of how I understand the topic from other explanations, experiments and real-life experience of a Python newbie.