The reason a priest exists, in whatever religion, is to offer sacrifice. Though God is capable of hearing the prayers of any person directly, it is fitting because of His dignity and holiness that He should have a special class of men set apart and consecrated to His service and worship alone. In this way they can attend to God with single-mindedness and without the distractions that would be attendant upon a man still living in the world. 

   In the Catholic Church, this “practical” reason for the priesthood is superceded by a more foundational “sacramental” reason: it is through the priesthood that Christ is made present to the Church and that His grace is distributed through the sacraments. Without the priesthood, we would have no sacraments.

For Further Discussion: Why Priests? Priesthood in the Old Testament; Priesthood Not Abolished but Transformed; Grades of Holy Orders; The Indelible Character of Holy Orders; Form and Matter; In Persona Christi; Priesthood of All Believers; Disciplines; Male Priests Only