The Torah procedure for handling what we would call involuntary manslaughter seems very strange to our modern understanding. The killer flees to one of six Levite cities to escape the victim's next of kin who may kill him on sight. If the killer makes it to the city of refuge, the elders there take him back to the scene and conduct an inquiry. If there was no murderous intent, the killer returns to the Levite city where he must stay until the High Priest dies. If the victim's next of kin finds the killer outside the city walls, he may kill him. So the killer has been found innocent of murder and yet he may be killed on sight. Strange indeed.
To understand we must return to the beginning of the Bible. There we find two deaths both of which God punishes by exile. The first is the introduction of death into the Creation when Adam ate of the tree of the knowledge of good and evil and the second is the murder of Abel.
By stretching a bit, we can see how Adam might have been guilty of manslaughter rather than murder, but what are we to do with Cain?
There are couple of possible explanations. Cain may not have understood that his actions could result in death. After all, there had been no human death until that point. Cain may simply have been fighting with his brother to take out his frustration, not realizing the consequences could be lethal. Alternatively, one might say that there was yet no specific prohibition against murder, so the only just punishment was exile. This thought is bolstered somewhat by God's protection of Cain when he complained that the punishment was too harsh.
So, if we consider God's imposition of exile in the first two cases of human death, we can view the city of refuge teaching as commentary on them. Consider the Levites as representatives of God within the Land of Israel. They ajudicate the case and then provide sanctuary to the killer who is exiled from his home. This correlates nicely with the disposition Adam's and Cain's cases.
The teaching in Numbers, however, adds an element - that the exile only lasts until the death of the High Priest "who was anointed with the holy oil". In the Hebrew, the word for anointed is, of course, Messiah. Thus the cities of refuge teach us that our exile lasted only until the death of the Messiah (who is a priest according to the order of Melchizedek).