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Muscles ache after exercise because of the production of lactic acid.
When you exercise, the muscles contract and produces lactic acid.
Muscles usually produce energy by using oxygen which means aerobically. When you exercise body need more oxygen but sufficient oxygen is not available and thus muscles produce energy anaerobically. Lactic acid is the by-product of the anaerobic process.
Oxygen is required to convert glucose into energy. But in insufficient oxygen, glucose is broken without oxygen that results in lactic acid.
The body normally adapts to aerobic environment, but when we perform intense exercise then body will not able to meet energy requirements immediately. Thus, lactic acid is produced as an alternative source of energy.
Therefore, we must train our body to tolerate intense exercise. If we increase our exercise then our body will be adapted to that rate at higher and muscles take more time to be exhausted.