Why do I care?  When planting crops or plants, soil density is very important. If the soil is packed too tightly, the plant or crop won't be able to absorb any water or nutrients from the soil and will not be able to grow properly.  Density in the atmosphere is also important in the formation of clouds and precipitation.

How does this relate to agriculture? 

Density can be used to explain variations in soil textures.  Think of the three main types of soil particles: sand, silt and clay.  To help you imagine the size of each of these types of particles, imagine that each particle of sand is the size of a bowling ball, each particle of clay is the size of a baseball, and each particle of silt is the size of a marble.

Now imagine that a swimming pool is filled with only sand (bowling balls) and try to picture how many of those bowling balls it would take to fill the whole swimming pool. Then, think about the space around each bowling ball, and imagine that the space is filled with air. That pool is not very dense, because there are lots of air pockets.  Now, imagine that you fill the spaces in between each bowling ball with clay (baseballs).  Your swimming pool just got a bit denser, with fewer spaces for air.  Now, if you fill in the remaining spaces with silt (marbles) there should be very few spaces left that are filled with air.  This last kind of soil is the most dense.

Soil that is very dense and has few air pockets has become this way through compaction.  Compaction makes it harder for water and air to penetrate the soil around the roots of your crop, which  makes it hard for the plants to grow.  Compacted soil results in less root growth, because it creates a barrier that makes it difficult for roots to have access to oxygen, water, and nutrients from the soil.  On the other hand, compacted soil is a good thing when it comes to things like building roads or buildings.  Construction engineers work very hard to compact soil in order to lend stability to structures.