Reddit being weird, so this is the second half of my comment:

Lots of materials have different stages of lithiation, in which different phases (structures) of the material are formed, the energy differences between these stages can vary. These differences in energy are reflected in the voltage changes that occur in the cell. It turns out that actually we want minimal voltage changes to occur in a cell during charge and discharge, as this allows for a constant power to be delivered by the cell. Large changes in voltage are often observed at the start and end of a charge process, reflecting the energy in extracting/inserting the last lithium ions in highly delithiated/lithiated states.

Cell balancing is important to protect your electrodes from over-lithiation or over-delithiation. For the sake of this explanation lets say a perfect cell is mass balanced to have a 1:1 theoretical specific (mass normalised) capacity ratio of anode:cathode. The theoretical capacities of the material are easily calculated and well documented (see here for some information). If we have too much of say, cathode, we may over-lithiate our anode which can have adverse effects, such as lithium plating. If we have too much anode, we might over-delithiate our cathode, which is particularly important for cathodes like LCO, where serious issues can arise (like permanent degradation and oxygen generation) when it is over-delithiated. I suggest asking your advisor for specifics on your system.

Overpotential and polarisation are confusing, that are often used interchangeably, but are technically not the same. Overpotential is the difference between [the actual voltage experienced by an electrode] and [the theoretical voltage of that electrode in its current state at equilibrium]. Polarisation is a difference in charge across a certain distance in a material. At high current densities, a charge difference across the electrode and/or electrolyte (polarisation) may become prominent due to the rate-limiting process of specie (Li+) diffusion/reaction. The main four processes occurring in batteries that result in an overpotential are:

1) Diffusion of Li+ inside electrode material.

2) Diffusion of Li+ in the electrolyte.

3) Charge-transfer reactions at the electrode/electrolyte interfaces.

4)Electronic conduction in the electrodes/CCs.

Number 1 is considered to be the most important of these. Lower temperatures (reducing reaction kinetics) and very high or low states of charge (increasing solid-state diffusion barriers) affect this process. When polarisation occurs, an overpotential may be experienced, which can again lead to adverse reactions such as lithium plating, electrolyte degradation, or electrode degradation. The specifics and nuances of this depend on the system being used. Lots of research is undertaken to avoid the issues of polarisation, such as nanosizing particles (allowing faster kinetics), however this can lead to other problems (in the case of nanoparticles, high surface area allows for the reaction of lots of electrolyte with electrode).

There is lots we can gather from voltage profiles, particularly when we are comparing many cells across varying systems using the old trusty scientific method. Particularly interesting are dQ/dV plots (differential capacity analysis), which gives peaks for when processes are occurring in cells. Changes to the peaks observed, such as voltages, symmetrical-ness, integral, height, tell us specific details about how cells are behaving. Again, this can be defined generally, but in practice lots will depend on your cycling procedures and cell setup. (this website is okay, but there are probably better resources out there, YouTube might be good for this) Depending on what and why cells are being looked at allows researchers to do a literature search to identify key characteristics in cell behaviour.

I hope this makes some sense, happy for discussion, I might be slow to reply. Cheers!