Oxygen acts as the final electron acceptor at the end of the electron transport chain.
In the electron transport chain, an electron gets passed from one enzyme to another until it reaches the final electron acceptor in the series: oxygen. Once the oxygen molecule picks up the electron, it combines with two hydronium ions to become water.
Think of a relay race, where Oxygen is the final member of the team to accept the baton before the finish line. Because Oxygen wants to accept the electron at the end of the chain, there is incentive for the electron to get passed from one enzyme to another until it reaches the terminal electron acceptor. In this way, Oxygen encourages the continuous flow of the electron down the chain.
By accepting low-energy electron at the end of the chain, oxygen also frees up the chain so that it can then accept another electron.