How and why does the distance between 2 electrodes affect the rate of electrolysis?

 Nothing, in terms of the chemistry. 

The distance between the electrodes affects the electrical resistance very slightly. Increasing the distance increases the resistance and reduces the current slightly, which reduces slightly the amount of product. 

For most practical applications, for electrolysis done in a beaker, varying the distance between the electrodes will make little difference. 

Increasing the concentration of the electrolyte will increase the current flow because there are more charged particles to carry charge, and increase the product yield.