Only a validly ordained priest can offer up the Holy Sacrifice of the Mass.
At every Mass, it is Jesus Who is both priest and victim. Since there is no time in God and He is an eternal “now,” Calvary is brought to us through the centuries. Jesus perpetuates His sacrifice through the sacramental priesthood.
At the Last Supper, after instituting the Holy Eucharist, He also ordained the apostles to the priesthood with the words, “Do this in memory of me.”
Christ ordained a male priesthood because the priests are to act In Persona Christi, or in the Person of Christ. The priests are the vehicles through which Christ continues His saving work. At Mass it is Christ who takes the bread, blesses it, breaks it, and gives it to the world. The priest is the mere instrument of Christ.
Deacons may proclaim and preach the word of God and distribute Holy Communion that was consecrated at a Mass previously. A religious sister, brother, or nun may also lead a celebration outside of Mass and also distribute Holy Communion consecrated at another Mass.
This permission was given by the Holy See to areas where a priest may only celebrate the Mass infrequently so as not to deny the people the graces of the sacrament of Holy Communion.