Gram staining targets the cell wall and a layer called peptidoglycan. Since human cells do not have cell walls or peptidoglycan, the gram stain would do nothing because the primary stain would wash out, notes Wikipedia.
The process of gram staining is used to differentiate between gram-positive and gram-negative bacteria, notes Sciences 360. A gram stain test uses a crystal violet dye and a counterstain, such as safranin. If the bacteria sample is gram-positive, the crystal violet dye is retained. If the bacteria sample is gram-negative, the counterstain is then visible under a microscope.
When human cells are stained, the crystal violet dye washes out and the counterstain clings to the nucleus of the cell. The colors then stain the layer of peptidoglycan if a cell wall is present. Peptidoglycan is a polymer located within the cell walls of bacteria. When iodine is added to the heat-fixed sample, the crystal violet dye binds to the iodine and is trapped in the cell.
The main difference between a gram-positive and gram negative cell is the thickness of the peptidoglcyan layer in the cell wall. Gram-positive cells have a very thick and compact peptidoglycan layer, while gram-negative cells have a very thin and less compact peptidoglycan layer.