What is a Minor Basilica?
A Minor Basilica is a Church of historical and architectural value which has "particular importance for the liturgical and pastoral life" of some place. In essence, it is the Pope's Church in some place around the world. Minor Basilicas are specifically tasked with celebrating the feasts of the liturgical year with great care and attention. "The word of God is to be diligently proclaimed either in homilies or in special sermons. The active participation of the faithful is to be promoted both in the eucharistic celebration and in the celebration of the liturgy of the hours."
On numerous days of the year, "The faithful who devoutly visit the basilica and within it participate in any sacred rite or at least recite the Lord's Prayer and the profession of faith may obtain a plenary indulgence under the usual conditions."
In addition to excellence in the fostering of the Sacred Liturgy, Minor Basilicas are to be places of instruction in the Catholic Faith and evangelization.
All of these mammoth tasks are certainly beyond any priest. They are the universal work of the Church! For this reason, all the faithful of the parish are encouraged to be an active part of the mission of the Minor Basilica.
* Citations taken from the official text governing Minor Basilicas, Domus Ecclesiae.
So why a "Minor" Basilica?
Well, there are only four Major Basilicas: St. Peter's, St. John Latteran, St. Mary Major and St. Paul Outside the Walls. These four Churches are particularly connected to the Pope in history and in practice. All other Basilicas are thus "Minor" Basilicas.