A gene is declared differentially expressed if an observed difference or change in read counts or expression levels between two experimental conditions is statistically significant. (doi: 10.1089/cmb.2015.0205)
Differential gene expression defines the specific structure and function of a cell by causing certain genes to be active and certain other genes to become permanently inactive. That is why you will see different cells in the human body will appear and function differently.
For instance, every cell in the body contains the genes for hemoglobin. Then why is it so that only red blood cells are able to make hemoglobin? This is due to differential gene expression as those genes are activated that define this type of cell. The genes to produce hemoglobin are not activated in any other cell type whether it may be muscle cell or brain cell. Its only in the RBCs.
So, even though every cell contains the complete genome, the difference between cells is not due to the genes present within the nucleus but through the expression of specific genes in the cell that gives the cell its characteristic.