First of all, it is clear that the diagram is cyclic on purpose: the experimentator sweeps the potential "manually" at a specific rate.
An explanation may be that the chard shows what's going on in the
electrochemical reactions (redox specifically) and demonstrates the "connection" between the processes which are explained by Nernst equation, Fick's first law, and Faraday's law.
Depending on what you know about the analyte already, you can find the redox potential, the diffusion coefficient, the number of electrons per molecule oxidized or reduced, and the concentration. All from one chart/experiment.
The use in thermodynamics can be derived from the use of the governing laws: Nernst equation and Faraday's law are related to the Gibbs free energy, Fick's first law - to the continuity equation.
Additionally, u can estimate the efficiency of the electron transfer between the electrolyte/electrode interface. The sharp peak represents the efficient electron transfer. If the peak is broad it represents the sluggish electron transfer at electrodes.