You feel as if you are being thrown outward (away from the circle) due to inertia. Your body is moving in the direction the car is moving at any particular time and wants to continue moving in that direction. When the car turns your body's inertia works to keep your body moving forward, thus you feel as if you are being thrown outward. The same happens in the Scrambler ride at the Midway.
In the Scrambler ride, you end up moving very quickly in circles. Your body wants to keep moving forward, but the Scrambler ride turns in a circle. You then feel as if you are being thrown outward away from the circle. If you the unlucky person sitting on the outside of the ride seat, the person on the inside slides to the outside and squishes you into a pancake! :-)