In racing sports, the racing line is the route that must be taken in order to minimize the time taken to complete the course.
When analyzing a single corner, the optimum line is one that minimizes the time spent in the corner and maximizes the overall speed (of the vehicle) through the corner. If one used the path with the smallest radius, that would minimize the distance taken around that corner. However, by fitting a curve with the widest possible radius into the corner, the higher speed which can be maintained more than compensates for the extra distance travelled.
The apex or clipping point is the innermost point of the line taken through a curve. The apex is often, but not always, the geometric center of the turn. Hitting the apex allows the vehicle to take the straightest line and maintain the highest speed through that specific corner. It is often near the tightest part of a corner.