For the analysis of water electrolysis, we shall use HO  ions (also known as oxonium ions) at the cathode, as an example to explain the traditional reactions.
Water molecules self-ionize to HO and OH ions. Near the cathode surface (within the double layer region), newly generated HO ions become hydrogen gas after obtaining electrons from the cathode; however because there is nearly no electric field inside the bulk solution (see section "Electric field distribution"), OH ions can only transport through the bulk solution very slowly by diffusion. Moreover, in pure water the intrinsic HO concentration is only 10 mol/L, not enough to neutralize the newly generated OH ions. In this way OH ions accumulate locally at the cathode surface (turning the solution near cathode into alkaline). Due to Le Chatelier's principle for water self-ionization,
the OH ions accumulation impede further self-ionization of the water, which reduces the hydrogen evolution rate and eventually prevents water electrolysis. In this case water electrolysis becomes very slow or even halts; this manifests as a large equivalent resistance between the two electrodes.
This is why in the macrosystem pure water cannot be electrolyzed efficiently - the fundamental reason is the lack of rapid ion transport inside the bulk solution.