Physical significance of chemical potential and fugacity
The chemical potential is the partial derivative of the Gibbs free energy with respect to the number of moles of the specified species at constant T, P, and numbers of moles of all other species.  The equation you wrote is the what this partial derivative reduces to for a species in an ideal gas mixture, where P is the partial pressure of the species in the mixture.  For a real gas, the fugacity of the species replaces the partial pressure of the species in the same equation for the chemical potential.