Reaction rate helps relate then change in concentration of reactants and products over time Note that the [[Molar Concentration]] $C=\frac{N}{V}$ where V is the volume of the mixture Hence $\frac{dN}{dt}=V\frac{dC}{dt}$ Substituting in above equation after dividing by $dt$ $\frac{dN_i/dt}{\nu_i^{''}-\nu_i^{'}} = d\xi/dt$ $\frac{dC_i/dt}{\nu_i^{''}-\nu_i^{'}} = \frac{d\xi/dt}{V} = \omega$ $\omega$ is the reaction rate. Reaction rate is a characteristic of the entire reaction. It is rate of advancement of reaction per unit time and per unit volume. You can relate reaction rate to molar/mass rate of depletion production of a species $\frac{dC_i}{dt} = \omega(\nu_i^{''}-\nu_i^{'})$