Density - the idea
Density is a measure of how tightly packed something is. For instance, snow is loosely packed as it falls and lands on the ground, but if you scoop up a bunch and press it together in your hands, the snowball you make is much denser – it is the same amount of material packed into a smaller space.
In chemistry we discuss the smallest particles of matter (atoms and molecules) so in chemistry, density is a measure of how tightly packed the molecules and/or atoms are.
We care about density in chemistry, because how tightly packed the molecules or atoms are will have an effect on the behavior of different materials. For instance, the less tightly something is packed the more easily it will mix with (and potentially react with) something else. In addition, things that are less dense will float in something that is more dense.