The charge discharge curves of a battery intersect at a particular value of voltage. As number of cycles increase, this intersection voltage changes. What is the significance of its value?
If we try to reformulate this question in more regular terms (and also build graphs of voltage changes not in the same way as the author said, but both voltages vs. degree of charge of the battery), we will see that for each degree of charge there is some difference between both discharge and charging voltages. This value depends on the densities of charge and discharge currents. It is equal to the sum of overvoltages during discharge and charge battery, and depends on its internal resistance. Since the internal resistance increases during cycling (if this did not happen, the battery would cycle forever), in the author’s viewpoint the “intersection point” is shifted. The direction of its shift will be determined by which of the overvoltages grows faster during battery cycling. This is definitely a conclusion. But is it enough to understand the causes of battery degradation?
It depends on the discharge/charge capacity you get from the cycling of your batteries that, generally, decreases upon cycling. That is due to the degradation of the electrodes you are using, for example if your battery configuration is LiFePO4/Li, the changes in profiles depends on degradation of the cathode, Li-anode and/or degradation of the electrolyte you are using.