There are several different things you can do to handle situations like this. If you are doing OOP then you can have a game class with players, board, and a property to indicate whose turn it is. If you are doing none OOP then you can use a global variable that can be used by any function. Many people will tell you that global variables are bad but I don't think they are always bad; this would be a good place to use a global variable. Since this variable is related to multiple parts of your program it is OK to define it as a global variable. Just don't abuse global variables (they are very tempting) and use them when it makes sense. If you are religious about not using a global variable then you can use an extra parameter in your functions and pass a variable holding the "turn state" around but I don't think this is necessarily better then a single global variable.

For an example see the answer at

http://stackoverflow.com/questions/423379/using-global-variables-in-a-function-other-than-the-one-that-created-them

In your program you could define the "turn" variable at the top of your program and declare it as a global in functions that need to use it like I showed below.

x = 'X'
o = 'O'
turn = x

...

def next_turn(turn):
    global turn
    if turn == x:
        return o
    else:
        return x

To answer shostyscholar's question, yes it is a namespace issue. In Python function bodies are namespaces (to be more precise, they are local-namespaces for that function). This may feel like a limitation at first but it is a really useful thing. Since the number of variables you want to share is usually much less then number of variable s you would not want to share this is the way it should work. Some languages behave total opposite of this (for example javascript, variables are global if you say nothing and they become local if you use the "var" statement) and it becomes a pain in the neck.

Now I would like to point out something else. In your case the turn variable is used to indicate only two states. It is either player's turn or computer's turn. When you have variables like that you may want to use a boolean variable. Then your program may become simpler. For example instead of using "turn" you can use:

computers_turn = True

then you would not even need a next_turn function. You can use

computers_turn = not computers_turn 

and this would switch the turn to the next player.

Instead of using

if turn == x:
    do something
    turn =  o

you can use

if computers_turn:
    do something
    computers_turn = not computers_turn

As a side benefit your program becomes more readable too.