What's the advantage of using yield in __iter__()?

Without generator functions, you would have to implement something like this, if you want to follow best practices:

In [7]: class IterableContainer:
   ...:     def __init__(self, data=(1,2,3,4,5)):
   ...:         self.data = data
   ...:     def __iter__(self):
   ...:         return IterableContainerIterator(self.data)
   ...:

In [8]: class IterableContainerIterator:
   ...:     def __init__(self, data):
   ...:         self.data = data
   ...:         self._pos = 0
   ...:     def __iter__(self):
   ...:         return self
   ...:     def __next__(self):
   ...:         try:
   ...:              item = self.data[self._pos]
   ...:         except IndexError:
   ...:             raise StopIteration
   ...:         self._pos += 1
   ...:         return item
   ...:

In [9]: container = IterableContainer()

In [10]: for x in container:
    ...:     print(x)
    ...:
1
2
3
4
5

Of course, the above example is contrived, but hopefully you get the point. With generators, this can simply be:

In [11]: class IterableContainer:
    ...:     def __init__(self, data=(1,2,3,4,5)):
    ...:         self.data = data
    ...:     def __iter__(self):
    ...:         for x in self.data:
    ...:             yield x
    ...:
    ...:

In [12]: list(IterableContainer())
Out[12]: [1, 2, 3, 4, 5]

As for state, well, it's exactly that - objects can have state, e.g. attributes. You can manipulate that state at runtime. You could do something like the following, although, I would say it is highly inadvisable:

In [19]: class IterableContainerIterator:
    ...:     def __init__(self, data):
    ...:         self.data = data
    ...:         self._pos = 0
    ...:     def __iter__(self):
    ...:         return self
    ...:     def __next__(self):
    ...:         try:
    ...:              item = self.data[self._pos]
    ...:         except IndexError:
    ...:             raise StopIteration
    ...:         self._pos += 1
    ...:         return item
    ...:     def rewind(self):
    ...:         self._pos = min(0, self._pos - 1)
    ...:

In [20]: class IterableContainer:
    ...:     def __init__(self, data=(1,2,3,4,5)):
    ...:         self.data = data
    ...:     def __iter__(self):
    ...:         return IterableContainerIterator(self.data)
    ...:

In [21]: container = IterableContainer()

In [22]: it = iter(container)

In [23]: next(it)
Out[23]: 1

In [24]: next(it)
Out[24]: 2

In [25]: it.rewind()

In [26]: next(it)
Out[26]: 1

In [27]: next(it)
Out[27]: 2

In [28]: next(it)
Out[28]: 3

In [29]: next(it)
Out[29]: 4

In [30]: next(it)
Out[30]: 5

In [31]: it.rewind()

In [32]: next(it)
Out[32]: 1