Look at the diagram.
Let the car of mass m travel at uniform speed v. At each point along its path, the persons inside car continue to move along straight line at speed v, due to Inertia Let there be a curve to the left with a radius of curvature R.
When the car turns left, the persons continue to travel along the tangential lines 1, 2, 3, 4 at the respective points. This is due to inertia of moving along a straight line and uniform velocity, in the same direction. The passengers experience a pull away from the curve towards outside of circle. Role of inertia of direction is to take the person in the tangential direction to circular path.
For the persons to go in the curve, to turn left, they need a force (Centripetal force ) needs to be given to them. So when the person holds the seat, door and pushes it away or pulls it forward, the person gets force F in the direction of radius R. So centripetal force F is supplied, for him to change direction and give centripetal acceleration.