Domestic Church in Encyclopedia of Catholic Doctrine, Our Sunday Visitor, 1997 (Ed: Russell Shaw)
The Church is the instrument of salvation. Christ lives and works in and through his Church in order to save and sanctify us, communicating his life and love and mercy, making us sisters and brothers of his, daughters and sons of God. Through the Church we enter into the "Family Life" of the Blessed Trinity.
It is doubly significant that the family is frequently referred to as the "domestic church". The Church herself has an essentially family nature. Life - supernatural life - begins and is nurtured in the Church, just as happens with natural life in the family. The family is in many ways like the Church in miniature, for supernatural life is of course also nurtured in the family. The graces of the sacrament of matrimony are there to help the spouses realize that the family they are forming is an instrument of redemption, for themselves and for their children; and that they are called to be active collaborators with Christ in this task.
In any true family people are humanized; they grow in human virtues and in humanity. In a christian family they are supernaturalized aa well: supernatural virtues and supernatural life develop in them.
People are helped to acquire a deeper sense of community - union in Christ - by worshipping together in their local church. Members of families however are not likely to acquire that community sense at church, if they are not living it at home - in the domestic church. It is there first of all that they have to sense the presence of Christ, pray to him, serve him, and love him in others.