Identifier for cells. Mhc is a marker on each cell, which tells our immune system whether the cell is our own or "foreign" (an infection or a transplant), and our body tries to destroy the "foreign" cells. This is great to get rid of infection, but also why transplants can be rejected. To minimize the risk of rejection, transplant doctors try to find donors with mhc similar to the patient's, often within the family.
Cell surface protein. The mhc are a series of glycoproteins on the surface of all nucleated (not red blood) cells in the body. They are also called hla (human leukocyte antigens). There are hundreds, they come from genes on the sixth chromosome, and they are inherited from each parent. They can trigger an immune response against foreign invaders (bacteria, viruses, etc.), as well as rejection of organs or tissues.