H&E stands for hematoxylin and eosin. These are two stains commonly used on tissue samples so that they can be seen under the microscope. Hematoxylin sticks to DNA which turns the nucleus blue or purple. Eosin sticks to proteins and other parts of the cells which turns them pink or red.
When tissue samples are cut and placed on a slide for examination under the microscope by a pathologist, the tissue is so thin that it is almost invisible. In order for your pathologist to be able to see the tissue, it needs to be stained with a dye give it colour.
The combination of these two stains allows pathologists to distinguish between different types of cells and even different parts inside the same cell. Abnormal cells tend to look different than normal cells when stained with hematoxylin and eosin which makes this stain very powerful for everyday use in pathology.