There are two ways in which dry air is referenced to in meterology:
One definition of dry air is the theoretical sample of air that has no water vapor. When looking at tables in meterology textbooks you will notice that for the composition of gases in the atmosphere there will often be a table that shows the abundance of each major gas within dry air. This is done since water vapor is a variable gas (ranging from a trace to about 4%). The amount of water vapor in the air depends on the dew point of the air. When water vapor is ignored what is left is a fairly fixed percentage of the percent by volume or percent by mass of Oxygen, Nitrogen and Argon. However, air in the atmosphere will not be perfectly dry since even in very cold air there will still be a trace of water vapor.
Another definition of air is air that has a low relative humidity. When the relative humidity drops below about 40% the air feels dry to skin. If very low relative humidity persists it can make the skin dry, lips chapped and can put more static in the air. In the winter when air with a low dew point from outside is heated and brought inside the air will decrease in relative humidity. To add moisture to the air some people will buy humidifiers. Although this air is referred to as dry air it is not perfectly dry. In some cases air will be referred to as dry even when the outside relative humidity is high but the dew point is low. This is because even if the air has a high relative humidity of 90% outside once that air is brought inside and heated the relative humidity will decrease significantly In situations in which the dew points are low outside (less than around 32 F) that air will often be referred to as dry by weather forecasters especially if the skies are clear.