A liturgical comb is a decorated comb used ceremonially in both Catholic and Orthodox Christianity during the Middle Ages, and in Byzantine Rite to this day.
The exact use of liturgical combs during the Middle Ages remains unclear. They may have been used in the ceremony accompanying the consecration of a bishop, or before or during the celebration of Mass.

Source : Wikipedia

Although it's known that Liturgical Combs were generally used for the ritual preparation of the priest before the celebration of the Mass, their origins, and any possible practical reasons for their development, are not known.