The height of a mountain determines, approximately, the density of air on its summit. As air becomes less dense, it contains less gases per unit of volume, and therefore less oxygen. Physiologists use this information to predict the oxygen deprivation a mountaineer faces at high altitude. For the most part, this relationship works quite well. But factors other than altitude also effect the density of air.
Temperature also changes the density of air.
As air gets warmer it expands and becomes less dense, causing atmospheric pressure to fall. In addition, air within the atmosphere can rise and fall, changing the atmospheric pressure. In fact, meteorologists monitor atmospheric pressure at the Earth's surface in order to determine whether the pressure is rising or falling, which helps to predict weather patterns. High pressure often represents stable air, while low pressure can signify instability. On a cold, sunny day there will be a significantly higher atmospheric pressure than when a big storm is moving in on a hot and humid day.