Why do electrolytic concentrations affect voltage in electrochemical cells? I know that the voltage of a cell is calculated via the Nernst Equation as $$E_\text{cell}=E^\circ-\frac{RT}{nF}\ln Q_\mathrm r$$ where $Q_\mathrm r$ represents $\frac{\text{concentration at the anode}}{\text{concentration at the cathode}}$. 

However I don't understand how these concentrations actually affect the potential difference. Could anybody explain the physical processes that mean changing the concentrations affect the voltage of the cell?
Potential is work to move charge and this work is done by the chemical energy stored in the reactants, so if the concentration of reactants increases then there are more reactants which will do more work so this implies that potential increases with comcentration.