Anaerobic respiration occurs when there is no oxygen available and so produces an oxygen debt. This debt is equivalent to the total amount of oxygen required to oxidise the lactic acid formed from this process into carbon dioxide and water. In other words, to cancel out the debt of oxygen owed.
Repaying this oxygen debt is vital as lactic acid is toxic and a build up in our cells and muscles can lead to harmful effects if not converted to CO2 and water quickly enough.
The existence of an oxygen debt explains why we continue to breathe deeply and quickly for a while after exercise.