In respiration, as you know the electrons travel through the electron transport chain and provide the energy to pump Hydrogen ions across the inner membrane. Once they reach the end of the chain, where do they go? This is where oxygen is needed: it 'accepts' the electrons, so is reduced. Without oxygen, the electrons would build up and prevent any more electrons from travelling through the chain.
Oxygen has another use; when hydrogen ions flow down their electrochemical gradient through ATP synthase, they need to be removed otherwise the concentration will build up and prevent the further flow of ions. So, oxygen also accepts hydrogen ions. When hydrogen ions, electrons and oxygen react together, you get water. This is why in respiration one of the products is water.