One critical role that oxygen plays in the body is that it is used to oxidize our food, in the process of cellular respiration, thus releasing energy, which is eventually stored in ATP in the electron transport chain in mitochondria, and in glycolysis in the cytoplasm.
Carbohydrates and fatty acids are gradually broken down to simpler carbohydrates, and then oxidized in our cells … producing energy, carbon dioxide, and water. It’s basically a highly controlled process of burning our food that gives us the energy we need to live.
Another critical purpose oxygen plays is that it is part of the water molecule: cells are about 70-90% water by mass, and without water and its ability to form hydrogen bonds life would likely not be possible at all.
So in fact, because of the very high water content, the human body is mostly oxygen, by mass. You can be assured that it plays many, many important roles in the body, not just one.
Of course oxygen, in the form of O2, has many effects on the body – it is highly reactive, and so it has to be carefully handled to avoid tissue damage, especially from the more reactive oxygen species that sometimes result from metabolic processes.
On the other hand, as User pointed out, reactive oxygen species and oxygen halides are also purposefully produced during metabolism, and are used, together with specialized proteins, to kill harmful invasive bacteria in vacuoles contained within neutrophils.