This part of the Mass comes after the Confiteor (I confess):
Confíteor Deo omnipoténti, beátæ Maríæ semper Vírgini, beáto Michaéli Archángelo, beáto Ioánni Baptístæ, sanctis Apóstolis Petro et Páulo, ómnibus Sanctis, et vobis, fratres: quia peccávi nimis cogitatióne, verbo, et ópere: mea culpa, mea culpa, mea máxima culpa. Ideo precor beátam Maríam semper Virginem, beátum Michaélem Archángelum, beátum Ioánnem Baptístam, sanctos Apóstolos Petrum et Páulum, omnes Sanctos, et vos, fratres, oráre pro me ad Dóminum Deum nostrum
I confess to Almighty God, to blessed Mary ever Virgin, blessed Michael the archangel, blessed John the Baptist, the holy Apostles Peter and Paul, and all the saints, and to you, brothers, that I have sinned in thought, word and deed: through my fault, through my fault, through my most grevious fault. Therefore I beseech blessed Mary, ever Virgin, blessed Michael the archangel, blessed John the Baptist, the holy Apostles Peter and Paul, all the saints, and you, brothers, to pray to the Lord our God for me.
(Followed by the server saying the same, exchanging 'brothers' for 'father')
This is a general confession of sins, both past, absolved mortal sins, and any venial sins you currently are guilty of, but which don't merit damnation.
It is in this sense that the general absolution makes explicit the priestly intercession to God on behalf of the people (in concordance with the fact that he is about to offer the perfect Victim to the Father, "in persona Christi"2 Cor 2:10).
He then intercedes for the people:
Misereátur vestri omnípotens Deus, et dimíssis peccatis vestris, perducat vos ad vitam ætérnam. Amen.
May almighty God have mercy upon you, forgive you your sins, and bring you into life everlasting. Amen.
He then blesses the people with a gesture, saying:
Indulgéntiam, absolutiónem, et remissiónem peccatórum nostrórum, tríbuat nobis omnípotens et miséricors Dóminus.
May the Almighty and merciful God grant us pardon, absolution, and full remissions of our sins. Amen.
Mortal sins must be confessed:
John 20:21-23 He said therefore to them again: Peace be to you. As the Father hath sent me, I also send you. When he had said this, he breathed on them; and he said to them: Receive ye the Holy Ghost: whose sins you shall forgive, they are forgiven them; and whose sins you shall retain, they are retained."
This could be because one needs to be quite sure of their absolved state before recieving the Eucharist, that is, whether they are in a state of grace, period.
So that no one should be recieving the Eucharist without purity of conscience in that regard:
1 Corinthians 11:27-29 "Wherefore whosoever shall eat the bread or drink the cup of the Lord in an unworthy manner, shall be guilty of the body and the blood of the Lord. But let a man examine himself, and so let him eat of the bread, and drink of the cup. For he that eateth and drinketh, eateth and drinketh judgment unto himself, if he discern not the body [10:16 "body" and "blood of the Lord"] [i.e. from what is profane]"
This petition and intercession for forgiveness generally is not a 'Sacrament' but a general plea for mercy. And it is followed by prayers right up to the Kyrie Eleison (Lord have mercy) before the Mass begins to turn more doxological (worship-oriented).
This is why the Sacrament of Confession/Extreme Unction is still the only means of absolution of mortal sins—a general plea for mercy doesn't constitute said Sacrament. It amounts to a priestly prayer.
A good reason this doesn't absolve everyone is because literally anyone could be there at Mass. To pretend forgiveness of all sins would be impossible, since "if we confess our sins he is just and faithful to forgive."1 Jn 1:9 And we know the method he instituted for such: Confession.
I can't find any authoritative sources which speak to—or feel the need to—on this at this time.
EDIT: Ken Graham has sources in his answer which may be of help.