The enumerate() function adds a counter to an iterable.

So for each element in cursor, a tuple is produced with (counter, element); the for loop binds that to row_number and row, respectively.

Demo:

>>> elements = ('foo', 'bar', 'baz')
>>> for elem in elements:
...     print elem
... 
foo
bar
baz
>>> for count, elem in enumerate(elements):
...     print count, elem
... 
0 foo
1 bar
2 baz

By default, enumerate() starts counting at 0 but if you give it a second integer argument, it'll start from that number instead:

>>> for count, elem in enumerate(elements, 42):
...     print count, elem
... 
42 foo
43 bar
44 baz

If you were to re-implement enumerate() in Python, here are two ways of achieving that; one using itertools.count() to do the counting, the other manually counting in a generator function:

from itertools import count

def enumerate(it, start=0):
    # return an iterator that adds a counter to each element of it
    return zip(count(start), it)

and

def enumerate(it, start=0):
    count = start
    for elem in it:
        yield (count, elem)
        count += 1

The actual implementation in C is closer to the latter, with optimisations to reuse a single tuple object for the common for i, ... unpacking case and using a standard C integer value for the counter until the counter becomes too large to avoid using a Python integer object (which is unbounded).