This Pasuk describes a scenario where one has killed another unintentionally and he runs off to a city of refuge.
One must remain
in the city of refuge until the death of the Kohen Gadol.
What was the reason of one waiting until the death of the Kohen Gadol?
Comes the Rambam
(brought down by Rav Z. Pliskin) and explains that the nature
of a person who suffers a serious misfortune(death of a family
member), has his suffering a bit relieved if he sees that others
also have suffered in a similar way. And that all the bad things
are not only happening to him.
So when the Kohen Gadol died, it was a partial consolation for the relatives of the deceased, and they will no longer feel the great passion of revenge that they had before his death.
At times one may feel that his suffering is the greatest, yet he just has to open his eyes and see that there are those who suffer more than him.
For ones degree of inner pain is dependent on ones subjective evaluation of his own suffering.