Over potential -what and why ?
When I took P-Chem, decades ago, one experiment we had was using a dropping mercury electrode, DME. I don't recall the details, but the set-up was fairly elaborate, especially compared to a Ag/AgCl electrode. The DME is fairly common (or was, before we decided that Hg was probably better avoided by the undergrad). The reason WHY we used it was it provided a CLEAN surface. Think about it. We wouldn't go to such great lengths if the problem of contamination wasn't significant. 

All materials absorb contaminants, may chemically react with near-by chemicals (solvent, ions, gasses), and will form a charge polarization layer, especially in polar solvents like H2O. In fact some electrochemical methods rely on it. But for getting the "pure" ideal thermodynamic (reversible) numbers the large tendency of electrode surfaces to change is a real problem. 

Overpotential is the term we use to describe the additional energy (voltage) we have to put in to these non-ideal systems (either at the anode or the cathode) to overcome these "side reactions". This energy is ultimately converted (mostly) to heat. Although maybe not an overpotential issue, surface area can be important, so smoothness does matter.

I can think of no area in chemistry (short of biochem) where you have to get into the weeds (details) so quickly as you do with electrochemistry. I wonder if its because chemistry is actually about electric interactions between atoms, molecules, ions, etc.? I should also mention that on other nice thing about the DME was that the surface was smooth - although I can't recall whether the surface was smooth at the atomic level, most solids are far from smooth, another problem in reproducibility.