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The proton motive force arises from a combination of the concentration gradient of protons and a voltage gradient across the membrane (the protons are positively charged, so an imbalance of protons means that the side of the membrane with more protons has a positive charge relative to the side with fewer protons).
One sees the tapping of proton motive forces particularly in both cellular respiration and photosynthesis, where they are used to generate ATP. Figure legend: The line in the middle represents a semipermeable membrane which does not permit movement of the protons (H+) across, i.e., as equivalent to a lipid bilayer.