How does the @property decorator work in Python?

The property() function returns a special descriptor object:

>>> property()
<property object at 0x10ff07940>

It is this object that has extra methods:

>>> property().getter
<built-in method getter of property object at 0x10ff07998>
>>> property().setter
<built-in method setter of property object at 0x10ff07940>
>>> property().deleter
<built-in method deleter of property object at 0x10ff07998>

These act as decorators too. They return a new property object:

>>> property().getter(None)
<property object at 0x10ff079f0>

that is a copy of the old object, but with one of the functions replaced.

Remember, that the @decorator syntax is just syntactic sugar; the syntax:

@property
def foo(self): return self._foo

really means the same thing as

def foo(self): return self._foo
foo = property(foo)

so foo the function is replaced by property(foo), which we saw above is a special object. Then when you use @foo.setter(), what you are doing is call that property().setter method I showed you above, which returns a new copy of the property, but this time with the setter function replaced with the decorated method.

The following sequence also creates a full-on property, by using those decorator methods.

First we create some functions and a property object with just a getter:

>>> def getter(self): print('Get!')
... 
>>> def setter(self, value): print('Set to {!r}!'.format(value))
... 
>>> def deleter(self): print('Delete!')
... 
>>> prop = property(getter)
>>> prop.fget is getter
True
>>> prop.fset is None
True
>>> prop.fdel is None
True

Next we use the .setter() method to add a setter:

>>> prop = prop.setter(setter)
>>> prop.fget is getter
True
>>> prop.fset is setter
True
>>> prop.fdel is None
True

Last we add a deleter with the .deleter() method:

>>> prop = prop.deleter(deleter)
>>> prop.fget is getter
True
>>> prop.fset is setter
True
>>> prop.fdel is deleter
True

Last but not least, the property object acts as a descriptor object, so it has .__get__(), .__set__() and .__delete__() methods to hook into instance attribute getting, setting and deleting:

>>> class Foo: pass
... 
>>> prop.__get__(Foo(), Foo)
Get!
>>> prop.__set__(Foo(), 'bar')
Set to 'bar'!
>>> prop.__delete__(Foo())
Delete!

The Descriptor Howto includes a pure Python sample implementation of the property() type:

class Property:
    "Emulate PyProperty_Type() in Objects/descrobject.c"

    def __init__(self, fget=None, fset=None, fdel=None, doc=None):
        self.fget = fget
        self.fset = fset
        self.fdel = fdel
        if doc is None and fget is not None:
            doc = fget.__doc__
        self.__doc__ = doc

    def __get__(self, obj, objtype=None):
        if obj is None:
            return self
        if self.fget is None:
            raise AttributeError("unreadable attribute")
        return self.fget(obj)

    def __set__(self, obj, value):
        if self.fset is None:
            raise AttributeError("can't set attribute")
        self.fset(obj, value)

    def __delete__(self, obj):
        if self.fdel is None:
            raise AttributeError("can't delete attribute")
        self.fdel(obj)

    def getter(self, fget):
        return type(self)(fget, self.fset, self.fdel, self.__doc__)

    def setter(self, fset):
        return type(self)(self.fget, fset, self.fdel, self.__doc__)

    def deleter(self, fdel):