The black bordering is the envelope of the picture tube. The picture tube has to withstand the high atmospheric air pressure, because the glass envelope is evacuated. In older TVs, a special glass or plastic shields were placed before the picture tube to protect any glass from hitting the viewer in case of an implosion.
But modern TVs incoporate implosion protection without any shield. In one arrangement a metal rim band called kimcode is held around the tube by a tension strap. The black bordering is nothing but this metal band for implosion protection, which prevents the glass from spilling over if the implosion happens.