For us in Western cultures, it is up to the individual to decide. In the Middle East, however, there is a group based honor. As far as I can gather, an individual can dishonor the group and the reputation of the group. In the case of honor killings, by killing the one who acted dishonorably, you are saying, "We, as a group, disapprove of their action", and thereby restoring honor to the group.
More information about text formats