Cornering force acts perpendicularly towards the center of the turn, relative to the direction of travel of the tires when turning.
When turning, the car does not move in the direction of the tires, but in a slightly different direction.
This angle is called the slip angle. Cornering force is shown by the red line below.
The sum of the cornering forces of each tire becomes a centripetal force, which balances the centrifugal force.
The cornering force also increases according to the slip angle up to a certain point, but if the slip angle increases further, the cornering force decreases.
This is because kinetic friction is smaller than static friction.