Aerobic respiration needs oxygen. Glucose is broken down completely and the products are carbon dioxide and water. The word equation is glucose + oxygen → carbon dioxide + water, and the symbol equation is C6H12O6 + 6O2 → 6CO2 + 6H2O. It releases a large amount of energy from each molecule of glucose.
Anaerobic respiration happens without oxygen. Glucose is only partly broken down, so much less energy is released. In human muscle cells the product is lactic acid. In yeast and plant cells the products are ethanol and carbon dioxide, and in yeast this is called fermentation.
During hard exercise the blood cannot supply oxygen as fast as the muscles use it, so the muscles respire anaerobically as well. Lactic acid builds up and causes muscle fatigue. After exercise, extra oxygen is needed to break the lactic acid down. This is called the oxygen debt, and it is why you keep breathing fast and deeply for a while.