Apostolicity is a quality of the Church, not just of the clergy. By going on pilgrimage, the believer imitates Christ, joining with other believers, living and dead. This apostolicity is a natural consequence of the liturgical dimension:
Apostolic dimension. The pilgrim’s journey, in a certain sense, recalls the journey of Christ and his disciples as they travelled throughout Palestine to announce the Gospel of salvation. In this perspective, pilgrimage is a proclamation of faith in which pilgrims become “errant heralds of Christ”( Apostolicam actuositatem 14).
The Directory on Popular Piety and the Liturgy is online at the Vatican site.