Question

Why is the atmospheric pressure lower on a high mountain peak than at sea level

Answer 1

The earths gravity attracts the molecules and collects the most near the surface. They all have weight and therefore have more pressure at the surface, as well. As you go higher, the attraction becomes less and these molecules some times fly off into space. This layer of equilibrium has the least of weight or pressure. 

The various pressures are measured by precision instruments called barometers or pressure sensors and expressed in inches of mercury or millibars. Air has a weight too, although not very much, If you "pile" the air mile high, the bottom pressure is heavier because of all the air sitting on top of it, therefore the pressure decreases with altitude, because there is less air "piled up" 
An analogy would be the same with water.

Planes have these instruments that tells the crew the altitude above sea level they are at when flying.