Your question made me curious, so I looked in some real-world code: the Python standard library. I found 67 examples of nested functions. Here are a few, with explanations.

One very simple reason to use a nested function is simply that the function you're defining doesn't need to be global, because only the enclosing function uses it. A typical example from Python's quopri.py standard library module:

def encode(input, output, quotetabs, header = 0):
    ...
    def write(s, output=output, lineEnd='\n'):
        # RFC 1521 requires that the line ending in a space or tab must have
        # that trailing character encoded.
        if s and s[-1:] in ' \t':
            output.write(s[:-1] + quote(s[-1]) + lineEnd)
        elif s == '.':
            output.write(quote(s) + lineEnd)
        else:
            output.write(s + lineEnd)

    ...  # 35 more lines of code that call write in several places

Here there was some common code within the encode function, so the author simply factored it out into a write function.

Another common use for nested functions is re.sub. Here's some code from the json/encode.py standard library module:

def encode_basestring(s):
    """Return a JSON representation of a Python string

    """
    def replace(match):
        return ESCAPE_DCT[match.group(0)]
    return '"' + ESCAPE.sub(replace, s) + '"'

Here ESCAPE is a regular expression, and ESCAPE.sub(replace, s) finds all matches of ESCAPE in s and replaces each one with replace(match).

In fact, any API, like re.sub, that accepts a function as a parameter can lead to situations where nested functions are convenient. For example, in turtle.py there's some silly demo code that does this:

    def baba(xdummy, ydummy):
        clearscreen()
        bye()

    ...
    tri.write("  Click me!", font = ("Courier", 12, "bold") )
    tri.onclick(baba, 1)

onclick expects you to pass an event-handler function, so we define one and pass it in.