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 3) 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 3) 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',)