These variations are extremely important to both meteorologists and aviators, as they strongly determine the different properties of the atmosphere.
For example, on a cool day, an airliner might have no problem safely departing a medium length runway, but on a warmer day, the density altitude might be higher, require a higher ground speed and true airspeed prior to liftoff, which would require more acceleration, a longer runway, and a reduced climb rate after liftoff.
In meteorology, departure from standard day conditions is what gives rise to all weather phenomena, including thunderstorms, fronts, clouds, even the heating and cooling of our planet.
But other factors, such as humidity, further alter the nature of the atmosphere, and are also defined under standard day conditions: The first three properties are usually referred as "standard day" conditions, which the viscosity aspect is largely ignored throughout the aviation community.
Because it is a key component of drag, it affects the amount of fuel burned per unit of distance travelled.