The most important use of oxygen is for breathing. Animals require
oxygen in their air (or water) to live.
Another use for oxygen is for oxidation reactions -- the most obvious
example is burning. Fires require oxygen to burn. Some fire extinguishers
work by preventing oxygen from reaching the burning materials. By adding
oxygen (more than is in the air) to a fire it will burn hotter. This is
how an oxy-acetylene torch works. The additional oxygen makes the flame
much hotter and it can effectively cut metal (by melting it).