<s>[INST] What does ** (double star) and * (star) do for Python parameters? In the following method definitions, what does the * and ** do for param2?
def foo(param1, *param2):
def bar(param1, **param2):

 [/INST] The *args and **kwargs is a common idiom to allow arbitrary number of arguments to functions as described in the section more on defining functions in the Python documentation.
The *args will give you all function parameters as a tuple:
In [1]: def foo(*args):
   ...:     for a in args:
   ...:         print a
   ...:         
   ...:         

In [2]: foo(1)
1


In [4]: foo(1,2,3)
1
2
3

The **kwargs will give you all 
keyword arguments except for those corresponding to a formal parameter as a dictionary.
In [5]: def bar(**kwargs):
   ...:     for a in kwargs:
   ...:         print a, kwargs[a]
   ...:         
   ...:         

In [6]: bar(name='one', age=27)
age 27
name one

Both idioms can be mixed with normal arguments to allow a set of fixed and some variable arguments:
def foo(kind, *args, **kwargs):
   pass

Another usage of the *l idiom is to unpack argument lists when calling a function.
In [9]: def foo(bar, lee):
   ...:     print bar, lee
   ...:     
   ...:     

In [10]: l = [1,2]

In [11]: foo(*l)
1 2

In Python 3 it is possible to use *l on the left side of an assignment (Extended Iterable Unpacking):
first, *rest = [1,2,3,4]
first, *l, last = [1,2,3,4]

Also Python 3 adds new semantic (refer PEP 3102):
def func(arg1, arg2, arg3='default', *, kwarg1='abc', kwarg2='xyz'):
    pass

Such function accepts only 2 positional arguments, and everything after * can only be passed as keyword argument, not positional one.
In Python 2 similar was true for all parameters after *args.
 </s>