The explanation for spatial variations in precipitation centers on the concept of relative humidity. The relative humidity is the water vapor pressure (numerator) divided by the equilibrium vapor pressure (denomator) times 100%. The equilibrium vapor pressure occurs when there is an equal (thus the word equilibrium) flow of water molecules arriving and leaving the condensed phase (the liquid or ice). Thus there is no net condensation or evaporation (Alistair Fraser, PSU).
Now, if the water vapor pressure is greater than the equilibrium value (numerator is greater), there is a net condensation (and a cloud could form, say). And that is not because the air cannot hold the water, but merely because there is a greater flow into the condensed phase than out of it.
Relative humidity describes the amount of water vapor actually in the air (numerator), relative to the maximum amount of water the air can possibly hold for a given temperature (denominator). It is expressed as a percentage:
If the relative humidity (RH) is 100%, this means that condensation would occur. On a typical hot muggy summer day, RH might be around 60-80%. In a desert, RH is commonly around 15-25%.
One important consequence is that when air masses change in temperature, the relative humidity can change, even if the actual amount of water vapor in the air does not (the numerator in our equation, which is defined by the saturation curve, stays the same, but the denominator changes with temperature). Figures 11-13 below show an example of this process. As the air cools, the relative humidity increases. If the air mass were cooled enough to become saturated (hit the solid black curved line), condensation would occur. This temperature is called the dew point.
In the same way, changes in relative humidity occur when warm moist air is forced to rise or, conversely, when cool dry air descends. For example, when an air mass moves over mountains, it cools as it rises, and when it reaches the dewpoint, water will condense. This forms clouds, and if the air mass cools enough, the condensation becomes rapid enough to form precipitation.