The answer is air pressure. Let's use the example of boiling a pot of water and cooking noodles. You likely know that the boiling point of water is 100 degrees C (212 degrees F), but this depends on the air pressure. The boiling point of water that we know as 100 degrees C is defined at sea level. The higher your altitude, the less air pushing down on you and the lower the air pressure.
At an altitude of 1000 feet the air pressure is about 97% of that at sea level. At 2000 feet the air pressure is about 93% of that at sea level. At 5000 feet, almost a mile above sea level, the air pressure is about 83% of that at sea level. What does this have to do with cooking?
Consider a boiling pot of water. To boil the water one needs to raise the temperature of the water enough such that the water turns into water vapor. The water can more easily turn into water vapor if the pressure pushing down on the water is less. Therefore, it is easier to boil water at higher elevations because the temperature needed is lower. A higher temperature causes the water molecules to move faster. With less air pressure pushing down, they don't need to move as fast to escape (become water vapor), and the water boils at a lower temperature.
Once the water starts to boil, you can't increase the temperature any further. If the water boils at a lower temperature and you dump your noodles in the water, the noodles are cooking at a lower temperature. As a result, it will take longer to cook the noodles.
How much lower is the boiling point of water at higher elevations? At 1000 feet the boiling point of water is 98.9 degrees C which is not much lower than the 100 degrees C at sea level. Thus there is no need to change the cooking instructions at this altitude. At 5000 feet, however, the boiling point of water has dropped to 94.9 degrees C which is significant drop. Many people live at even higher elevations with even lower boiling points. Therefore there is a need to adjust cooking times at higher elevations.