Why does your car swerve while driving?

Because you have "play" in your steering wheel. Your steering mechanism is routed through a gear box. The gears in this box wear down over time creating "play" in the steering. Your steering wheel and your front wheel are no longer synchronized.

This play allows you to move your steering wheel a few inches either way without actually moving the wheels. It also allows the wheels to have just as much free time as the steering wheel causing you to be almost constantly correcting the path of the car to stay in a straight line. This is why your car will move out of a straight line when you are pointing your steering straight ahead.

Also, it is a road hazard because if you have to slam on your brakes you may not stay in a straight line. The "play" will allow the front of the car to violently go to the left or right.