Hydrogen ions drive ATP synthase in photosynthesis. This happens when hydrogen ions get pushed across the membrane creating a high concentration inside the thylakoid membrane and a low concentration in the cytoplasm.
Because of osmosis H+ will force itself out of the membrane through ATP synthase. Using their kinetic energy to escape, the protons will spin the ATP synthase which in turn will create ATP.
This happens in cellular respiration as well though the concentrated membrane will instead be the inner membrane of the mitochondria.
Hydrogen ions concentration, measured as pH, is also responsible for the acidic or basic nature of a compound. Water molecules split to form H+ and hydroxide anions. This process is referred to as the self-ionization of water.