Altitude sickness (AMS) is brought about by climbing to high altitudes where there is little air pressure than required. There is a great calculator here https://baillielab.net/critical_care/air_pressure/ that calculates atmospheric pressure in reference to altitude.
When you reach the peak of Mount Kilimanjaro air pressure decreases to a mere 49%. This means that every air that you inhale, contains about half amount of oxygen. Due to the respiratory strain that this brings to your respiratory system, it is advised to take it slow on the mountain. As you do not want fluid to build up in your lung cavities causing pneumonia and the gap between the brain and the skull causing severe headaches and migraines. The result can be fatal at times.
With great emergency precautions and great acclimatization practices, we will help minimize or avoid altitude sickness (AMS). Read more here about altitude sickness and acclimatization rules.