Density gradient is a spatial variation in density over an area. The term is used in the natural sciences to describe varying density of matter, but can apply to any quantity whose density can be measured. 
A steep density gradient in a body of water can have the effect of trapping energy and preventing convection, such a gradient is employed in solar ponds. In the case of salt water, sharp gradients can lead to stratification of different concentrations of salinity. This is called a Halocline. 
In the life sciences, a special technique called density gradient separation is used for isolating and purifying cells, viruses and subcellular particles. Variations of this include Isopycnic centrifugation, Differential centrifugation, and Sucrose gradient centrifugation. A blood donation technique called Pheresis involves density gradient separation.
The understanding of what is at the centre of the earth, the earth core, requires the framework of density gradients in which elements and compounds then interact. Fast breeder nuclear reactor at the core of the earth is one theory by reason of density gradient and supported and espoused by J. Marvin Herndon (7 & 8).
In the study of population, the density gradient can refer to the change in density in an urban area from the center to the periphery. 
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- 7. Herndon, J. Marvin (1994) Planetary and Protostellar Nuclear Fission: Implications for Planetary Change, Stellar Ignition and Dark Matter Proceedings: Mathematical and Physical Sciences, Vol. 445, No. 1924 (May 9, 1994), pp. 453–461
- 8. Herndon, J. Marvin (1996) Substructure of the inner core of the Earth Vol. 93, Issue 2, 646-648, January 23, 1996, PNAS