What is the equation that shows what happens at the cellular level when you breathe?

Its called the formula for Cellular Respiration. Human breathing is critical to making this process work.  The end point of Cellular Respiration is the ATP, or energy molecule.  Why does this matter?  What happens when you quit breathing?  Cells in the brain stop producing ATP and very quickly the brain starts to have problems!

Oxygen + Glucose   yields Carbon Dioxide + Water + Energy

O2        + C6H12O6  ->    CO2               +  H20   + ATP

For plants, the process is paired up with Photosynthesis as they can both make their own food and transform the food into energy the organism can use.

Carbon Dioxide + water + energy yields Oxygen + glucose

CO2               + H2O   + sunlight ->   O2         + C6H12O6

Cool deal, as these two equations are easy to remember as opposites!