Consider the displacement of aqueous silver ions by copper metal:
Cu + 2 Ag+ → Cu2+ + 2 Ag
ΔHorxn for this process is -147.2 kJ and ΔGorxn is -88.3 kJ. Based on our established criteria, this process will be spontaneous at standard states. One way to look at these two energy terms is this:
ΔH represents the total amount of energy that must be transferred to the surroundings in order to keep the temperature of the system at 298 K

ΔG represents the part of that total energy which can be harnessed to do useful work during the transfer, i.e., the energy "free" to do work
From this we might say:

ΔH = ΔG + "unfree" energy