So what is the Liturgy of the Hours?

 NOT *just* for Priests, Religious or Clergy ..... 

Are the Faithful also required to pray the Divine Office? No, but when they do, they join with the entire Church throughout the world in its common prayer, sanctifying the day and night, giving praise and worship to God in a rich and beautiful tradition of our Catholic heritage. We are all one in the Body by virtue of our Baptism.. how wonderful to join with those around the world with the same words, at the same time, praising our glorious Triune God! 

The celebration of the Divine Office, as an act of the whole Church, even when prayed in solitude, enjoys Christ’s presence in those gathered. The Liturgy of the Hours, like the Mass and other liturgical celebrations of the Church, are sacred acts of the whole Church and of Christ present in the Church. The Eucharist and the Divine Office belong to the whole Church, to all those who by reason of their baptism share in the life of Christ.
Christ, therefore, is truly present when the Divine Office is celebrated, especially so in the Psalms and other scripture texts. We take it for granted–in the sense that we in fact believe–that Christ is present in the Eucharist, but sometimes we need reminding that Christ is also present in the Liturgy of the Hours.

The Liturgy of the Hours is the prayer of the whole People of God. In it, Christ himself “continues His priestly work through his Church.” His members participate according to their own place in the Church and the circumstances of their lives. The laity, too, are encouraged to recite the divine office either with the priests, among themselves, or individually.
The celebration of the Liturgy of the Hours demands not only harmonizing the voice with the praying heart, but also a deeper “understanding of the liturgy and of the Bible, especially of the Psalms.”

The hymns and litanies of the Liturgy of the Hours integrate the prayer of the psalms into the age of the Church, expressing the symbolism of the time of day, the liturgical season, or the feast being celebrated. Moreover, the reading from the Word of God at each Hour with the subsequent responses or troparia and readings from the Fathers and spiritual masters at certain Hours, reveal the deeper meanings of the mystery being celebrated, assist in understanding the psalms, and help one prepare for silent prayer. The lectio divina, where the Word of God is so read and meditated that it becomes prayer, is thus rooted in the liturgical celebration.
The Liturgy of the Hours, which is like an extension of the Eucharistic celebration, does not exclude but rather (in a complementary way) calls forth the various devotions of the People of God, especially adoration and worship of the Blessed Sacrament.

The worship “in Spirit and in truth” of the New Covenant is not tied exclusively to any one place. The whole earth is sacred and entrusted to the children of men. What matters above all is that, when the faithful assemble in the same place, they are the “living stones,” gathered to be “built into a spiritual house.” The Body of the risen Christ is the spiritual Temple from which the source of living Water emanates. Incorporated into Christ by the Holy Spirit, “we are the temple of the living God.”

Source: Catechism of the Catholic Church, Part Two, Section One, Chapter Two.