When life evolved, first came heterotrophs that obtained their organic molecules from their environment. Then came autrotrophs who made their own organic lecyles. The most important autotrophs are photosynthetic organisms. These photosynthetic organisms lived in the water and made glucose from CO2 and H2O. A byproduct of this reaction was O2.
Now, O2 killed off many of the species since it is very reactive. But the remaining species used the O2 for cellular respiration. Before, the cellular respiration was done anaerobically, without oxygen. The way this wroked was that the glucose was oxidated and the electrons from the glucose was used to make ATP, the main source of cellular energy. Once those electrons were used, they were deposited in a highly electronegative element compound, such as Nitrogen containing compounds. When plants produced O2, instead organisms doing anaerobic respiration, since oxygen is an extremely electronegative element, organisms deposited the electrons in the oxygen molecule. This is aerobic respiration. This from of respiration was more efficient and advantageous for land organisms. That is why we use oxygen.
Lungs and breathing is one of the many ways organisms obtain oxygen for delivering to cells to do cellular respiration. Fishes use gills. Most mammals use lungs. Many single celled organisms just obtain their oxygen through diffusion.