What does asterisk * mean in Python?

See Function Definitions in the Language Reference.

If the form *identifier is present, it is initialized to a tuple receiving any excess positional parameters, defaulting to the empty tuple. If the form **identifier is present, it is initialized to a new dictionary receiving any excess keyword arguments, defaulting to a new empty dictionary.

Also, see Function Calls.

Assuming that one knows what positional and keyword arguments are, here are some examples:

Example 1:

# Excess keyword argument (python 2) example:
def foo(a, b, c, **args):
    print "a = %s" % (a,)
    print "b = %s" % (b,)
    print "c = %s" % (c,)
    print args

foo(a="testa", d="excess", c="testc", b="testb", k="another_excess")

As you can see in the above example, we only have parameters a, b, c in the signature of the foo function. Since d and k are not present, they are put into the args dictionary. The output of the program is:

a = testa
b = testb
c = testc
{'k': 'another_excess', 'd': 'excess'}

Example 2:

# Excess positional argument (python 2) example:
def foo(a, b, c, *args):
    print "a = %s" % (a,)
    print "b = %s" % (b,)
    print "c = %s" % (c,)
    print args

foo("testa", "testb", "testc", "excess", "another_excess")

Here, since we're testing positional arguments, the excess ones have to be on the end, and *args packs them into a tuple, so the output of this program is:

a = testa
b = testb
c = testc
('excess', 'another_excess')

You can also unpack a dictionary or a tuple into arguments of a function:

def foo(a,b,c,**args):
    print "a=%s" % (a,)
    print "b=%s" % (b,)
    print "c=%s" % (c,)
    print "args=%s" % (args,)

argdict = dict(a="testa", b="testb", c="testc", excessarg="string")
foo(**argdict)

Prints:

a=testa
b=testb
c=testc
args={'excessarg': 'string'}

And

def foo(a,b,c,*args):
    print "a=%s" % (a,)
    print "b=%s" % (b,)
    print "c=%s" % (c,)
    print "args=%s" % (args,)

argtuple = ("testa","testb","testc","excess")
foo(*argtuple)

Prints:

a=testa
b=testb
c=testc
args=('excess',)

I only have one thing to add that wasn't clear from the other answers (for completeness's sake).

You may also use the stars when calling the function. For example, say you have code like this:

>>> def foo(*args):
...     print(args)
...
>>> l = [1,2,3,4,5]

You can pass the list l into foo like so...

>>> foo(*l)
(1, 2, 3, 4, 5)

You can do the same for dictionaries...

>>> def foo(**argd):
...     print(argd)
...
>>> d = {'a' : 'b', 'c' : 'd'}
>>> foo(**d)
{'a': 'b', 'c': 'd'}

All of the above answers were perfectly clear and complete, but just for the record I'd like to confirm that the meaning of * and ** in python has absolutely no similarity with the meaning of similar-looking operators in C.

They are called the argument-unpacking and keyword-argument-unpacking operators.