How does the control of gene expression lead to differentiation of cell function in multicellular eukaryotes?

Every cell of the organism has the same DNA sequence and same genes. However, not all genes are expressed in every single cell at the same time. Only those genes necessary for a specialised function of a specialised cell are expressed in the specialised cell. For example, skin cells have some different proteins than nerve cells. Genes responsible for those "skin proteins" are activated in skin cells and are turned off in nerve cells.