Also allows you to do this: (in short, invoking Outer(3).create_inner_class(4)().weird_sum_with_closure_scope(5) will return 12, but will do so in the craziest of ways.
class Outer(object):
    def __init__(self, outer_num):
        self.outer_num = outer_num
    def create_inner_class(outer_self, inner_arg):
        class Inner(object):
            inner_arg = inner_arg
            def weird_sum_with_closure_scope(inner_self, num)
                return num + outer_self.outer_num + inner_arg
        return Inner
Of course, this is harder to imagine in languages like Java and C#. By making the self reference explicit, you're free to refer to any object by that self reference. Also, such a way of playing with classes at runtime is harder to do in the more static languages - not that's it's necessarily good or bad. It's just that the explicit self allows all this craziness to exist.
Moreover, imagine this: We'd like to customize the behavior of methods (for profiling, or some crazy black magic). This can lead us to think: what if we had a class Method whose behavior we could override or control?
Well here it is:
from functools import partial
class MagicMethod(object):
    """Does black magic when called"""
    def __get__(self, obj, obj_type):
        # This binds the <other> class instance to the <innocent_self> parameter
        # of the method MagicMethod.invoke
        return partial(self.invoke, obj)
    def invoke(magic_self, innocent_self, *args, **kwargs):
        # do black magic here
        ...
        print magic_self, innocent_self, args, kwargs
class InnocentClass(object):
    magic_method = MagicMethod()
And now: InnocentClass().magic_method() will act like expected. The method will be bound with the innocent_self parameter to InnocentClass, and with the magic_self to the MagicMethod instance. Weird huh? It's like having 2 keywords this1 and this2 in languages like Java and C#. Magic like this allows frameworks to do stuff that would otherwise be much more verbose.
Again, I don't want to comment on the ethics of this stuff. I just wanted to show things that would be harder to do without an explicit self reference.