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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).
This generates a concentration gradient of charged ions across the membrane called an potential difference (if it's due to H+, it's called a proton motive force, if it's due to Na+ it's called a sodium motive force). This is a stored form of energy, the product of the respiration process. The ions can then flow back down the concentration gradient through specialised pores. The most common pores are ATPases, but they may also be things such as the mot proteins of bacterial flagella.