Explanation for different boiling points of water on different altitudes

Boiling point of water changes with altitude because atmospheric pressure changes with altitude.

So, how/why boiling point changes with pressure.There is good explanation of this at hyperphysics (with diagrams).

Now, why does pressure change with altitude? Imagine you are swimming in water. Deeper you go more pressure you feel, because there is more water above you.

$P = P_0 + \rho gh$

$P$ - pressure, $P_0$- pressure at the surface, $\rho$ - density of fluid, $g$ - gravity of Earth, $h$ - height/depth to free surface

There is huge column of air above our heads.

$\rightarrow h$ at sea level > $h$ at hill station.

$\rightarrow P$ at sea level > $P$ at hill station.

$\rightarrow$ boiling point at seal level > boiling point at hill station.

Boiling is a special case of evaporation. Any particle in the liquid state may evaporate. The puddles on your street evaporate, but have you ever seen a puddle boil? The gas formed by a substance that boils above room temperature is called vapour.

Boiling is the vigorous bubbling that occurs within a body of a liquid as it vaporizes internally. A bubble is a quantity of gas or vapour surrounded by liquid. Imagine a pot of water being heated. Some molecules at the bottom of the pot are receiving so much heat and consequently moving so fast that they bounce around pushing other water molecules away from them. This produces a bubble. The vapour pressure inside the bubble acts to inflate the bubble while the weight of the water and air above the bubble create an opposing pressure that acts to collapse the bubble. As the bubble rises, the water vapour molecules transfer their energy to the water molecules around the bubble. This causes the vapour molecules to lose energy so the bubble shrinks and collapses before it reaches the surface.

The entire pot of water is not yet boiling because it has not yet reached the boiling point. THis process continues, transferring energy from the bottom of the pot to the top until all the water molecules are moving as fast as possible without entering the gas phase. Only at this point, when the bubbles rise to the surface of the water without collapsing is the entire pot of water boiling. Just before breaking through the water's surface the bubble is only opposed by the atmospheric pressure above the liquid. One definition of boiling point is the temperature at which the substance's vapour pressure (the pressure inside the bubble) equals the surrounding air pressure. The air pressure above the sample could be lowered by placing the sample in a vacuum chamber or by taking it to a higher elevation. This would lower the the substance's boiling point because the bubbles would have less opposing pressure.

Boiling point is also defined as a substance's highest possible temperature in the liquid state at any given atmospheric pressure. It therefore represents the highest kinetic energy the substance's particles can possess in the liquid state. As the temperature of water approaches 100degC, more and more of the molecules have their maximum kinetic energy in the liquid state until at 100degC all the molecules are moving at the same maximum speed in the liquid state.

The boiling point of an element or a substance is the temperature at which the vapor pressure of the liquid equals the environmental pressure surrounding the liquid.
Atmospheric pressure is due to air above any given point. At greater heights, there is less air above you and hence pressure decreases.
Lesser pressure hence lower boiling points as you go higher.