Jamieson, Fausset and Brown on Leviticus 21:5

5. They shall not make baldness upon their heads ... nor ... cuttings in their flesh--The superstitious marks of sorrow, as well as the violent excesses in which the heathen indulged at the death of their friends, were forbidden by a general law to the Hebrew people (Le 19:28). But the priests were to be laid under a special injunction, not only that they might exhibit examples of piety in the moderation of their grief, but also by the restraint of their passions, be the better qualified to administer the consolations of religion to others, and show, by their faith in a blessed resurrection, the reasons for sorrowing not as those who have no hope.