Oxygen is a very powerful oxidising agent, which means it’s very good at taking electrons from other molecules (It’s so good at taking electrons from other molecules that the process of oxidation is named after oxygen). Many processes that happen in the body require an oxidising agent, and oxygen is a convenient one for the body to use. This is because there’s lots of it in the atmosphere, it’s powerful, and it’s small (so can easily be transported around the body).
Not all life needs oxygen, some bacteria found in polluted soil can use chemicals called chloroalkanes as an oxidising agent instead of oxygen. This is really interesting as chloroalkanes are normally considered as toxic waste product.