For the car to change direction when you turn the steering wheel, there has to be sufficient friction (grip) between the tyres and road surface. If the speed is too high or grip is not sufficient for the speed, there will not be enough 'force' to turn the way you want.

The need for centripetal force is a function of speed and mass (weight). The need for centripetal force increases with the square of the relative change in speed (if you double your speed, you quadruple the need for centripetal force). You as a driver therefore determine how great the centripetal force must be.

Lack of centripetal force may in worst case scenarios lead you to run off the road in a bend (which unfortunately is a very common traffic accident among young people).