Muscle soreness associated with strenuous exercise is at least partly due to

Anaerobic respiration resulting in oxygen debt, due to lactic acid accumulation.

Explanation:

After strenuous muscle activity extra oxygen is needed to re-convert lactic acid into glucose and ATP. As you exercise the liver anaerobically converts glucose to lactic acid and carbon dioxide this results in oxygen debts that needs to be repaid later.

Oxygen debt by definition is the amount of oxygen needed by muscles to oxidise lactic acid to glucose after muscle activity.