Vatican II teaches that all the faithful, who have the baptismal priesthood, can offer Jesus to the Father and unite themselves to Jesus, the perfect sacrifice; furthermore, pastors need to teach their flock this great mystery.
"The Church, therefore, earnestly desires that Christ's faithful, when present at this mystery of faith, should not be there as strangers or silent spectators; on the contrary, through a good understanding of the rites and prayers they should take part in the sacred action conscious of what they are doing, with devotion and full collaboration. They should be instructed by God's word and be nourished at the table of the Lord's body; they should give thanks to God; by offering the Immaculate Victim, not only through the hands of the priest, but also with him, they should learn also to offer themselves..." (Sacrosanctum Concilium, n. 48)
"Thus the Eucharistic Action, over which the priest presides, is the very heart of the congregation. So priests must instruct their people to offer to God the Father the Divine Victim in the Sacrifice of the Mass, and to join to it the offering of their own lives." (Presbyterorum Ordinis, n. 5)
The mystery was articulated at length by Pope Pius XII in his masterpiece encyclical on the liturgy, Mediator Dei (from 1947, a good 15 years before the Council). If you ever have the time, I strongly suggest reading it! Let me give you a lengthy excerpt (from nn. 84-93) which I believe will help to bear fruit in your prayers, most especially those which you offer at Mass.
Oh, but first, a bit of terminology will help here. A sacrifice has two parts: the death of the victim and the offering of the victim. The death is often called immolation (from the Latin immolare which means "to sacrifice"), and this is achieved in the Mass with the words of Consecration ("This is my Body", "This is my Blood"). The offering of the victim is often called oblation (from the Latin oblata, a form of offerre, which means "to offer"). The priest, and he alone by virtue of his ordination, is the minister of the immolation; but as Mediator Dei explains, all of the faithful share in the oblation.
Now onto the quote:
(84) [W]e deem it necessary to recall that the priest acts for the people only because he represents Jesus Christ, who is Head of all His members and offers Himself in their stead. ...
(85) However, it must also be said that the faithful do offer the divine Victim, though in a different sense. ...
(86) "Not only," says Innocent III of immortal memory, "do the priests offer the sacrifice, but also all the faithful: for what the priest does personally by virtue of his ministry, the faithful do collectively by virtue of their intention." We are happy to recall one of St. Robert Bellarmine's many statements on this subject. "The sacrifice," he says "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."
(87) Moreover, the rites and prayers of the eucharistic sacrifice signify and show no less clearly that the oblation of the Victim is made by the priests in company with the people. For not only does the sacred minister, after the oblation of the bread and wine when he turns to the people, say the significant prayer: "Pray brethren, that my sacrifice and yours may be acceptable to God the Father Almighty;" but also the prayers by which the divine Victim is offered to God are generally expressed in the plural number: and in these it is indicated more than once that the people also participate in this august sacrifice inasmuch as they offer the same. ...
(88) Nor is it to be wondered at, that the faithful should be raised to this dignity. ... [T]hey participate, according to their condition, in the priesthood of Christ.
(89) It is fitting, then, that the Christian people should also desire to know in what sense they are said in the canon of the Mass to offer up the sacrifice. ...
(90) First of all the more extrinsic explanations are these: it frequently happens that the faithful assisting at Mass join their prayers alternately with those of the priest, and sometimes - a more frequent occurrence in ancient times - they offer to the ministers at the altar bread and wine to be changed into the body and blood of Christ, and, finally, by their alms they get the priest to offer the divine victim for their intentions.
(91) But there is also a more profound reason why all Christians, especially those who are present at Mass, are said to offer the sacrifice.
(92) In this most important subject it is necessary, in order to avoid giving rise to a dangerous error, that we define the exact meaning of the word "offer." The unbloody immolation at the words of consecration, when Christ is made present upon the altar in the state of a victim, is performed by the priest and by him alone, as the representative of Christ and not as the representative of the faithful. But it is because the priest places the divine victim upon the altar that he offers it to God the Father as an oblation for the glory of the Blessed Trinity and for the good of the whole Church. Now the faithful participate in the oblation, understood in this limited sense, after their own fashion and in a twofold manner, namely, because they not only offer the sacrifice by the hands of the priest, but also, to a certain extent, in union with him. It is by reason of this participation that the offering made by the people is also included in liturgical worship.
(93) Now it is clear that the faithful offer the sacrifice by the hands of the priest from the fact that the minister at the altar, in offering a sacrifice in the name of all His members, represents Christ, the Head of the Mystical Body. Hence the whole Church can rightly be said to offer up the victim through Christ. But the conclusion that the people offer the sacrifice with the priest himself is not based on the fact that, being members of the Church no less than the priest himself, they perform a visible liturgical rite; for this is the privilege only of the minister who has been divinely appointed to this office: rather it is based on the fact that the people unite their hearts in praise, impetration, expiation and thanksgiving with prayers or intention of the priest, even of the High Priest himself, so that in the one and same offering of the victim and according to a visible sacerdotal rite, they may be presented to God the Father. It is obviously necessary that the external sacrificial rite should, of its very nature, signify the internal worship of the heart. Now the sacrifice of the New Law signifies that supreme worship by which the principal Offerer himself, who is Christ, and, in union with Him and through Him, all the members of the Mystical Body pay God the honor and reverence that are due to Him.