To go to the extreme and define it beyond how the Church intends it though is wrong, but that's never stopped anyone before.
You'll understand I am skeptical of accepting the definition of a few anomymous FR posters. I will accept; however, an official definition by the Catholic Church.
Well fine, the priest is alter Christus acting in persona christi
From the Cat:
In the person of Christ the Head . . .ADDRESS OF POPE JOHN PAUL II TO THE CLERGY OF ROME Thursday, 13 February 1997
1548 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 his 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:23
It is the 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).241549 Through the ordained ministry, especially that of bishops and priests, the presence of Christ as head of the Church is made visible in the midst of the community of believers.26 In the beautiful expression of St. Ignatius of Antioch, the bishop is typos tou Patros: he is like the living image of God the Father.27
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.25
1550 This presence of Christ in the minister is not to be understood as if the latter were preserved from all human weaknesses, the spirit of domination, error, even sin. The power of the Holy Spirit does not guarantee all acts of ministers in the same way. While this guarantee extends to the sacraments, so that even the minister's sin cannot impede the fruit of grace, in many other acts the minister leaves human traces that are not always signs of fidelity to the Gospel and consequently can harm the apostolic fruitfulness of the Church.
1551 This priesthood is ministerial. "That office . . . which the Lord committed to the pastors of his people, is in the strict sense of the term a service."28 It is entirely related to Christ and to men. It depends entirely on Christ and on his unique priesthood; it has been instituted for the good of men and the communion of the Church. The sacrament of Holy Orders communicates a "sacred power" which is none other than that of Christ. The exercise of this authority must therefore be measured against the model of Christ, who by love made himself the least and the servant of all.29 "The Lord said clearly that concern for his flock was proof of love for him."30
ADDRESS OF HIS HOLINESS BENEDICT XVI TO THE BISHOPS OF THE EPISCOPAL CONFERENCE OF ENGLAND AND WALES ON THEIR "AD LIMINA" VISIT Monday, 1st February 2010
Be close to your priests, and rekindle their sense of the enormous privilege and joy of standing among the people of God as alter Christus. In Newman’s words, “Christ’s priests have no priesthood but His … what they do, He does; when they baptize, He is baptizing; when they bless, He is blessing” (Parochial and Plain Sermons, VI 242)
BENEDICT XVI GENERAL AUDIENCE Wednesday, 24 June 2009
As an alter Christus, the priest is profoundly united to the Word of the Father who, in becoming incarnate took the form of a servant, he became a servant (Phil 2: 5-11). The priest is a servant of Christ, in the sense that his existence, configured to Christ ontologically, acquires an essentially relational character: he is in Christ, for Christ and with Christ, at the service of humankind.