Two definitions, for starters:
The mission of the Church pertains to the salvation of men, which is to be achieved by belief in Christ and by His grace.
The apostolate of the Church and of all its members is primarily designed to manifest Christ’s message by words and deeds and to communicate His grace to the world.
And a clarification:
This is done mainly through the ministry of the Word and the sacraments, entrusted in a special way to the clergy, wherein the laity also have their very important roles to fulfill if they are to be “fellow workers for the truth” (3 John 8). It is especially on this level that the apostolate of the laity and the pastoral ministry are mutually complementary.
People have their own take on what “mutually complementary” means. AA carefully makes the distinction of the “special” ministry of the Word and sacraments for the clergy, but lay people not only have “an” important role, but “their” important roles. What might these be?
The very testimony of their Christian life and good works done in a supernatural spirit have the power to draw men to belief and to God; for the Lord says, “Even so let your light shine before men in order that they may see your good works and give glory to your Father who is in heaven” (Matt. 5:16).
Lay people aren’t only involved in a passive showing of what they do. AA suggests we take initiative:
” … a true apostle looks for opportunities to announce Christ by words addressed either to non-believers with a view to leading them to faith, or to the faithful with a view to instructing, strengthening, and encouraging them to a more fervent life. “For the charity of Christ impels us” (2 Cor. 5:14). The words of the Apostle should echo in all hearts, “Woe to me if I do not preach the Gospel” (1 Cor. 9:16).”
So, we are to take to heart the apostolic calling of St Paul.
Since, in our own times, new problems are arising and very serious errors are circulating which tend to undermine the foundations of religion, the moral order, and human society itself, this sacred synod earnestly exhorts laymen-each according to his own gifts of intelligence and learning-to be more diligent in doing what they can to explain, defend, and properly apply Christian principles to the problems of our era in accordance with the mind of the Church.
These new problems and errors continue to this day, making AA all the more appropriate for extensive examination and study.