A graft versus host (GVH) reaction is a harmful immune system effect where lymphocytes within tissue that was grafted from a different individual attacks the tissue in its new location (i.e. the host's tissue). This typically occurs with bone marrow transplantations in which the donated bone marrow cells attack the tissues (often the kidneys) of the recipient.
This is similar to allograft immunity, where the reverse occurs. GVH reaction does not occur when perfectly matched tissues are transplanted, for instance syngenic and autologous bone marrow transplants.
From the science dictionary at http://biotech.icmb.utexas.edu/