A density column is simply a separation of substances based on density differences within a container. A common example that is often used is the separation of salad dressing into its layers. Say a dressing was made of vinegar (with density of 1.05 g/mL), water (with a density of 1.0 g/mL), and oil (with a density of .9 g/mL). We know that the items with lower densities float on top of denser items. Therefore, the oil would reside on the top, the water would be located in the middle, and the vinegar would be found on the bottom.
To answer your question, if the solid that was added was the same solid that was already a part of the density column, then that layer would simply be of a greater height. If you are adding a new and different kind of solid to the density column, then that solid and the ones already present would separate based on density differences (with the densest settling below those with lesser densities).