The short answer is that some muscles of the body ("fast twitch" muscles) don't have the same capability of storing and processing oxygen as other muscles. Due to that, and the fact that humans tend to breathe incorrectly or less efficiently during heavy exercise (thereby taking in less oxygen), the muscles continue to function by using lactic acid fermentation to produce ATP (by glycolysis). Below, there are a few web resources you can use for diagrams and deeper explanation.
It was found that when a normal and healthy humans is in a state of relaxation is inhaling from 6 to 8 liters of air per minute, of which about 0.3 liters of oxygen are transferred from the pulmonary socket to blood. Simultaneously, carbon dioxide is removed from the blood and expired. When the same person is involved in an activity which requires the most muscles, may inhale 100 liters of air per minute, from which to extract 5 liters of oxygen.
Normally, arterial blood contains about 18% oxygen, expressed by volume (transported by hemoglobin in red blood cells). If inhaling pure oxygen, this percentage increased to 18.5%. During resting tissues absorb oxygen at a rate which decreases to 18% the oxygen percentage from blood arteriosus to about 12% in venous blood. This is the arterio-venous difference.
On the other hand during exercises the blood can give to tissues up to 15% oxygen, nearly 2.5 times more than during relaxation. Biological properties of hemoglobin have an important role in adjusting the body during exercise.
In the past it was believed that muscle fever is due to "deposit" of lactic acid (a substance resulted from metabolism of carbohydrates to release energy needed to ATP restoration) which is supposed to be accumulated in muscle, following intense exercises. It turned out it was a wrong assumption, lactic acid is removed from the muscles more quickly, 98% being removed from the trained muscles, in about 1 hour and 30 minutes (with 50% in the first 15 minutes), so too quickly to lead to fever muscle for several days. Lactic acid actually cause muscle fatigue and not muscle fever.
Pulmonary ventilation is increased during physical exercise. In moderate exercise, ventilation increases in direct proportion to the amount of carbon dioxide formed. But during strenous exercise, lactic acid is also formed., and the resulting increase in arterial pH acts as an additional stimulus to pulmonary ventilation. These changes in Po2, Pco2 and pH, however, can account for only a small amount of increased respiration during exercise.
By ingenious cross circulation techniques exercise results in a marked increase in respiration even when the Po2, Pco2 and pH are artificially maintained at resting levels. This increase is caused by impulses reaching the respiratory centre from proprioceptors in the active skeletal muscles.