The Church says that the Priest acts "in persona Christi Capitis". Where is this term taken from?
It means: "in the person of Christ the Head [of the Church]".
Christ is the High Priest, in Whose person all other ordained priests act when they offer the Holy Sacrifice of the Mass.
When a Catholic priest consecrates the host and wine, he truly identifies Himself with Christ when he says "This is my body." and "This is my blood."
The sacrifice is principally offered in the person of Christ. Thus the oblation that follows the consecration is a sort of attestation that the whole Church consents in the oblation made by Christ, and offers it along with Him.
Sacrificium, inquit, in persona Christi principaliter offertur. Itaque ista oblatio, consecrationem subsequens, est quaedam testificatio, quod tota Ecclesia consentiat in oblationem a Christo factam, et simul cum illo offerat.
What does “in persona Christi Capitis” mean?
In persona Christi Capitis is a Latin phrase meaning "in the person of Christ the Head of the Church”, an important concept in Catholicism. A priest acts in persona Christi, because he acts as in the place of Christ. The term, In persona Christi capitis, “in the person of Christ the head of the Church,” was introduced in by the bishops of the Vatican Council II in the Decree on the Ministry and Live of Priests, Presbyterorum Ordinis, December 7, 1965.1
The office of priests, since it is connected with the episcopal order, also, in its own degree, shares the authority by which Christ builds up, sanctifies and rules his Body. Wherefore the priesthood, while indeed it presupposes the sacraments of Christian initiation, is conferred by that special sacrament; through it priests, by the anointing of the Holy Spirit, are signed with a special character and are conformed to Christ the Priest in such a way that they can act in the person of Christ the Head. (1)
The Catechism of the Catholic Church employs this expression in reference to the sacrament of Holy Orders.
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:
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).
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.
Only men may be ordained priests and are able to act in the person of Christ the Head of the Church.
It is also the reason why a woman cannot be a priest; for a woman can in no understandable way become a “father” to the Church or represent Christ in persona Christi. - A priest must be able to act in persona Christi capitis (in the Person of Christ the Head of the Church)