Consider a change of the energy of a system system, given the natural variable $S,V$ (entropy and volume):
$$dE = \delta W + \delta Q$$
Where $W$ is the mechanical work (volume change) and $Q$ is the energy changes via heat flux.
We know that the mechanical work exchanged from the system with the environment is link with volume change and pressure i.e. $W(P,V)$ and the thermal exchanges are dependant on the entropy and temperature i.e. $Q(T,S)$.
Now impose a constraint on your system imposing constant temperature $T_0$.
Obviously $\delta W=0$ during transformation your system will do in order to maximize it's Helmoltz free energy as the volums stays constant. Only heat exchanges will occur and $A$ will go to its maximum at equilibrium. What's left is the mechanical work you can extract from your system through volume changes (expansion work)!
Now impose a constraint on your system regarding the pressure and the temperature. Reaching the new equilibrium will force your system to go through temperature changes and volume changes until it reaches equilibrium so your system can't heat up anything (due to the reach of equilibirum temperature with heat bath) and you cannot extract mechanical work (due to the reach of equilibrium with pressure bath).
What you can extract though is chemical work through electricity (non expansion work).
You actually could already do this at constant volume though so you see that in the first case, you can still extract chemical and mechanical work (maximum possible work in your book), defined by Helmoltz Free energy, but in the second case, as in the equilibrium your system as already given it's mechanical work in order to reach equilibrium, you can only extract chemical work (non expansion work) represented by Gibbs free energy. That's why the later is often used to describe chemical reactions at constant temperature and volume.
I hope this helps.