In order to first answer this, it needs to be known that a gene is a sequence of genetic information within an organism's DNA which is translated by the cell into a protein. Proteins are long chains of amino acids which perform vastly various functions and take part in nearly every biological process.
When a gene is expressed within a cell, it means that that piece of DNA is translated within that cell to create the protein. Different kinds of cells express different proteins which assist the cell in performing their designated function, and don't express the proteins which are of no use to that cell.
When researchers wish to know which genes are expressed within the various different types of cells, they do this in order to understand what proteins are used within that cell. Understanding which proteins are created within a cell can allow the researchers to understand how exactly the cell performs its function.
Genes are the key to unlocking all kinds of things, from the functions of a single cell to an entire disease. That is why researches are so interested in genes.
As to why they need to know about the genotype of various cell types boils down to cell functions. On an overly simplified level all cells should be the same. We know however that they are not. Muscle tissue cells vary greatly from nuerons and likewise from blood cells. Knowing how to control and manipulate these differences could mean tremendous medical breakthroughs!
If the genes of a stem cell could be manipulated to turn the cell into say a liver cell, one could theoretically grow a new liver as oposed to having a transplant.