The clumping together of red blood cells is called agglutination. It occurs when antibodies in the plasma of one blood type bind to the antigens on the surface of another blood type's red blood cells, causing them to stick together and form clumps. This process is part of the body's immune response, as it helps to identify and attack foreign substances in the bloodstream. However, if it occurs during a blood transfusion or in the case of incompatible blood types, it can lead to serious complications such as organ damage or even death. Therefore, blood compatibility is an important consideration in medical procedures that involve the transfer of blood or blood products.