Anaerobic respiration is the breakdown of glucose without oxygen
The equation for anaerobic respiration is C6H12O6 → 2C2H5OH + 2CO2
The production of lactic acid during anaerobic respiration causes muscle soreness and fatigue, as the glucose molecule isn't fully broken up
Oxygen debt is when the body needs more oxygen to fully break apart the glucose molecules that weren't fully broken apart in anaerobic respiration. This is why we pant after running.
During anaerobic respiration, no matter how fast you breathe or how fast your heart is beating there is not enough oxygen getting into the body for aerobic respiration to provide enough energy / ATP
during hard exercise, both aerobic and anaerobic respiration takes place. This is because the body quickly uses up the oxygen being breathed in, so it has to revert to creating energy without using oxygen.