Cornering force is the sideways force produced by a vehicle tyre during cornering.
Tyre force is generated by tyre slip. In the case of cornering, tyre force is proportional to slip angle. Slip angle describes the deformation of the tyre contact patch, this deflection of the contact patch deforms tyre in a fashion akin to a spring.
As with deformation of a spring, deformation of the tyre contact patch generates a reaction force in the tyre; the tyre lateral force. Integrating the force generated by every tread element along the contact patch length gives the total tyre force. Although the term, "tread element" is used, the compliance in the tyre then leads to this effect is actually a combination of sidewall deflection and deflection of the rubber within the contact patch. The exact ratio of sidewall compliance to tread compliance is a factor in tyre construction and inflation pressure.
The diagram is misleading because the tyre force would appear to be acting in the wrong direction. It is simply a matter of convention to quote positive tyre force as acting in the opposite direction to positive tyre slip so that calculations are simplified, since a vehicle cornering under the influence of a tyre force to the left will generate a tyre slip to the right.