What special graces and powers does a priest receive through the Sacrament of Holy Orders?

The Priest: receives the power of forgiving sin and of offering the Holy Sacrifice of the Mass. He is made another Christ; a living representative of the Redeemer, Whose work he continues.

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Catholic AnswerThe priest receives all the graces that he needs to fulfill his role as an "alter Christus" (another Christ) for the people. As their priest he may perform all the sacraments, except Holy Orders. He may only administer Confirmation under special circumstances or with the permission of the his Bishop. The Sacrament of Holy Orders configures the recipient to Christ by a special grace of the Holy Spirit so that he may act as a representative of Christ in his triple office of priest, prophet, and King. He is configured to Christ as Priest, Teacher, and Pastor.

from The Catechism of the Catholic Church, second edition, English translation 19941548 In the ecclesial service of the ordained minister, it is Christ himself, who is present to his Church as Head of his Body, Shepherd of this flock, high priest of the redemptive sacrifice, Teacher of Truth. This is what the Church means by saying that the priest, by virtue of the sacrament of Holy Orders, acts in persona Christi Capitis; (Cf. Lumen Gentium 10; 28; Sacrosanctum concilium 33; Christus Dominus 11; Prsbyterorum ordinis 2; 6)

Is it he same priest, Christ Jesus, whose sacred person his minister truly represents. Now the minister, by reason of the sacerdotal consecration which he has received, is truly made like to the high priest and possesses the authority to act in the power and place of the person of Christ himself (virtute ac persona ipsius Christi). Pius XII, encylical, Mediator Dei: Acta Apostolicae Sedis, 39 {1947} 548)

Christ is the source of all priesthood: the priest of the old law was a figure of Christ, and the priest of the new law acts in the person of Christ. (St. Thomas Aquinas, Summa TheologiaeIII, 22, 4c.