The atmosphere is capable of holding tons of moisture that’s transported all across the world; a lot of which isn’t always present in the form of rain, snow, or any other precipitation. A lot of this moisture can be found being held up in the atmosphere just waiting for the right variables to come together to escape out of the clouds.
Precipitable water (PW) is defined in the AMS Glossary (roughly) as, the total amount of atmospheric water vapor found in a vertical column of unit-cross sectional area, if this water vapor were to be completely condensed into a liquid and collected in that same unit volume. Typically, this value is expressed in terms of height in inches.
To put it simply, it’s a measure of how much water can be condensed out and obtained from the top of the atmosphere to the surface at any given time.
ANALOGY: Think of it like having a giant sponge soaked with water. If you were to ring out that sponge, all the water that comes out of it would be the measure of water within that sponge. Precipitable water is sort of like that, only this water is in the atmosphere.
The image below shows Mesoscale Analysis Data showing precipitable water values at a given point in time:

Hopefully the diagram below will help make more sense out of all of that. The column on the left of the image shows water vapor contained within that space from the top of the atmosphere to the surface. The column on the right shows the amount of liquid water there would be within that same space if all the water vapor were condensed into a liquid.

For those of you who like math, this next part is for you.
Precipitable water can also be expressed in an equation such as the one below:

If x(p) describes the mixing ratio at a pressure level (p), then the precipitable water (W) is equal to 1 over the density of water (𝘱) times gravity (g), “contained in a layer bounded by” pressure levels 1 (p1 at the surface) and 2 (p2 at the top of the layer).
As a rule of thumb the greatest amount of water vapor is found near the Earth’s surface and decreases with height.
When the humidity is high, we can generally expect PW values to be high, which means any showers that come around are likely to be decent rain makers.
The largest precipitable water values in the entire globe come from over the equator and oceans in the tropics. This is due to having larger amounts of moisture available and evaporation occurring, therefore putting more water content into the atmosphere. In areas with high PW values, you typically find more clouds in the sky and more precipitation occurring. You will not have high PW values over a desert.
You can see in the Total Precipitable Water Loop below from 2012 shows higher PW values over the equator in the darker green colors swirling around the globe.

The higher the precipitable water values, the more moisture is available in the atmosphere to produce rainfall. Think this: values below 1” typically mean “dry,” and anything at 1” or above means “wet.”

NOTE: Precipitable water does NOT indicate how much rain a given location will receive. It’s more than common to have rainfall totals MORE than 1″ in an area with precipitable water of 1″ since PW values are an instantaneous value, while convergence of moisture can occur and produce even more rain over a long period of time.
Model data can map out what precipitable water values will look like in the future. For example, the loop below shows a model run from the North American Mesoscale (NAM) model of what precipitable water values will do after a cold front pushes through the area.
Oftentimes cold fronts will bring the “last leg” of showers and even some storms before drier, cooler, and less humid air moves in to replace the moisture ridden atmosphere that was in its place before. You can see how the values drop from around 2 inches to around 0.5 inches below:

When forecasting, meteorologists don’t only want to know the moisture content at the surface, which is measured by dew point and humidity, but they want to know the amount of moisture aloft as well. It can be very important when forecasting the potential for heavy rain, and flooding concerns when PW values are high and a good amount of rain is in the forecast.