From the White Wolf Wiki, the most complete White Wolf reference

A Blood Hunt is an order given by the local prince, calling for the Final Death of a Kindred. Such an order is usually given whenever a Kindred poses a serious threat to the Masquerade, however, there may also be other reasons.

Any Kindred who hears the order is expected to participate in the Hunt, although it's not required. Typically, the damned have until midnight to escape the city. If they don't, then they are open to retribution by their fellow Kindred.

If any Kindred provides assistence to the damned, they possibly become a target of the Blood Hunt as well.