Ok think of the case where the AI moves some game pieces around. The AI is running in it's own thread.
While the AI is moving the game pieces around, the games draw routine is called.
The AI hasn't finished it's run, so some pieces are in the right place, and some are in the wrong place. It's even possible for one of the coordinates of a piece to have been updated but not the others. This will produce horrible on screen artifacts.
So you need to plan for this situation and have a way of handling it.
An even more dangerous example is when you have AI and physics running in their own threads. Hell that can go wrong spectacularly