Chemiosmotic hypothesis states describes that the ATP generated during cellular respiration is mostly produced by the proton electrochemical coupling inside the mitochondria and chloroplast of the cell.
In the process of ATP synthesis, initially the hydrogen+ ions (protons) are transported from the mitrochondrial matrix to the space between the inner and outer membranes. These hydrogen ions are transported by some carrier proteins. The membrane proteins that are capable of carrying protons across the cell membrane or mitochondria are known as proton pumps.
Thus, in Chemiosmotic Hypothesis, the function of proton pumps is to carry hydrogen+ ions (protons) from the mitochondrial matrix to outside.