The processes of cellular respiration and breathing are part of the same process. When you inhale, carbon dioxide is replaced by oxygen in your blood; this oxygen is required by cells to perform aerobic cellular respiration as opposed to anaerobic cellular respiration--a similar process that does not require oxygen.
Breathing
When you inhale, air is drawn into your lungs by the movement of your diaphragm and other breathing muscles. Air enters your lungs via your nose or mouth and down your windpipe to be divided into each lung by your trachea. As air enters the lung, it is channeled down ever smaller pathways, similar in shape to an upside-down tree. At the end of these pathways are tiny air sacs called alveoli. It is here that oxygen in your inhaled air is transferred into your blood while carbon dioxide, a byproduct of your cells breaking down nutrients, is excreted, replacing the oxygen. As you exhale, this carbon dioxide is expelled into the environment. This process is repeated in every breath you take.
CELLULAR RESPIRATION
Oxygen drawn into your blood by your lungs is used in the process of aerobic cellular respiration, an "exergonic" process meaning it produces energy for your body. This energy is drawn from glucose in your cells and is released as a substance known as adenosine triphosphate (ATP). ATP is a form of energy that cells can use to perform their basic functions. In simple terms: glucose + oxygen = carbon dioxide, water and ATP (energy).