The ability of a tissue to be grafted from a donor to a host, without the host's immune system attacking the grafted tissue. The chances of H2 histocompatibility is determined by how well the tissue proteins (cell surface glycoproteins in the tissue, to be specific) match between donor and host.
From the BioTech Dictionary at http://biotech.icmb.utexas.edu/. For further information see the BioTech homenode.