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When muscles pull or strain or stretch during a vigorous exercise, we feel a lot of pain. There is burning sensation in those muscles.

This sensation is due to lactic acid, which is produced in the muscles. Our body's response system tries to get more oxygen to the muscles. It is not possible to give sufficient oxygen immediately. So the muscles shift from aerobic (with oxygen) respiration to anaerobic respiration (without oxygen).  Both processes produce ATP.  Anaerobic respiration produces more toxins.

So liver has to do more work to remove the additional toxins. When sufficient oxygen is available to the muscles, the respiration shifts back to aerobic.

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A simple answer:

Our muscle cells have to break down the glucose to get energy to do something. But during heavy exercise, we need more oxygen but only a limited supply can go in. So, in this case, the cells starts respiring anaerobically(without oxygen). And in that process, the muscle cells produce Lactic acid as an end product. The acid could cause irritation and pain in the muscles. (See, in the presence of Oxygen, the lactic acid is completely broken down, but with CO2 it cannot)

To get relief, we can have a hot bath(sauna) or a good massage. This improves circulation and so O2 is being transported better so the lactic acid is completely broken down.
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