In most people, white blood cells are an important part of the immune system, which fights off initial infection and form antibodies to attack specific pathogens. However, in a leukemia patient, the white blood cells are created in uncontrolled quantities in both the bone marrow and the lymph nodes. In addition, the white blood cells formed are abnormal and useless in fighting off infection. As a result, the abnormal amount of white blood cells makes it impossible for the body to function properly, as well as lessening the body's ability to fight off real infections. In addition it poisons the liver which attempts to remove and process the abnormal cells.
The only cure for leukemia is a bone marrow transplant from a compatible donor, although it should be noted that the problem usually arises in abnormal white blood cells which then "hijack" the bone marrow rather than the bone marrow itself. As part of the preparation for the transplant, the patient must be given radiation therapy to totally destroy the patient's bone marrow, and with it the immune system, until the transplant can proceed.
In Family, Nick had leukemia and had already been given radiation therapy when it was learned the donor, his brother, had developed an illness as well. A sick donor cannot give bone marrow as any infection would quickly overwhelm the recipient's weakened immune system.