Technically an ascent of Kilimanjaro is classified as entry into the Extremely High altitude zone. Altitude is defined on the following scale: High Altitude Classification of Zones
No specific factors such as age, sex, or physical condition can be used to predict susceptibility to altitude sickness. Some get it and others simply don't. Most people can go up to 2,500 m without significant discomfort.
Air at sea level comprises about 21% oxygen, while the barometric pressure averages about 1 bar (1000 mbar). As altitude increases, the oxygen concentration remains the same but since the pressure falls the number of oxygen molecules per breath is reduced.
At 3,500 meters the barometric pressure is only about 630 mbar (depending on weather conditions), so there are roughly 40% fewer oxygen molecules per breath. In order then to supply adequate amounts of oxygen to your body your breathing rate - even while resting - must increase.
This extra breathing increases the amount of oxygen in the blood, but not to sea level volumes. Since the amount of oxygen required for activity is the same, the body must adjust itself to coping with less oxygen. This process is known as acclimatisation. Failure to give your body the opportunity to undergo this process may lead to a dangerous condition known as AMS, or acute mountain sickness.