The technical definition of density is mass per unit volume.  Generally, density describes how tightly packed something is.  An object with a lot of material in a small space is more dense than an object that has lots of air space included.  In the atmosphere, gas that is less dense has a lower concentration of molecules per volume than a denser gas and will tend to rise  compared to the air around it. For example, gasoline vapor is heavier than air molecules and so tends to stay near the ground when you fill up your gas tank, which can lead to a fire hazard if the lingering vapor encounters a spark.

Warm air is less dense than cooler air (depending on the humidity, since water molecules weigh less than air molecules).  This means that dry warm air tends to rise compared to areas of cool air around it.  You can notice the effects of this if you live in a two-story house as the upstairs tends to be warmer than the downstairs. Areas of warm rising air often result in the development of clouds and even precipitation in the regions where the vertical movement of air is strongest.

A hot air balloon is a good example of how people work with density (Figure B). Hot air balloons use the properties of density in order to float. In the base of the hot air balloon, there is a torch that heats up the air inside of the balloon. When the air inside the balloon becomes warmer than the surrounding air, the balloon will begin to float. The person controlling the hot air balloon can add more heat to the balloon to reach the desired height. The air inside the balloon needs to cool in order for the balloon to land.