Respiration is the process by which the body creates energy by breaking down nutrients. This can either happen in the presence of oxygen, or without it. The key difference between the two processes are that aerobic respiration requires oxygen and anaerobic respiration does not.
However there are more differences between the two processes.
Aerobic respiration creates relatively larger amounts of energy by breaking down sugars in the presence of oxygen creating water and carbon dioxide as products. This process is occurring constantly in plants and animals, and occurs in the mitochondria of you and I.
glucose + oxygen -> carbon dioxide + water
C6H12O6 + 6O2 → 6CO2 + 6H2O
Anaerobic respiration creates relatively smaller amounts of energy, but does not need oxygen. The same thing is broken down - glucose - but a different waste product - lactic acid - is made. In exercise when we can’t get enough oxygen to our muscles anaerobic respiration occurs and lactic acid is produced. Glucose is used less efficiently and not completely broken down so less energy is made. Furthermore the lactic acid needs to be oxidised to water and carbon dioxide later and needs oxygen to do this, so you are effectively “borrowing energy” that you will need oxygen for later on - this is referred to as the oxygen debt. Oxygen debt explains why you continue to breathe heavily after having stopped exercise.
glucose -> lactic acid
C6H12O6 → 2C3H6O3