I've been learning all I can about the prayers of the Church. Until we became Catholics, corporate prayer was basically saying the Lord's Prayer during the service, along with some miscellaneous other prayers that someone up in front prayed and we answered with "Lord, hear our prayer" (at least, that's how we did it when we were in the Presbyterian church). Corporate prayer was missing totally in the nondenominational churches we attended, unless you count the congregation listening to people praying personal prayers out loud.
I actually didn't even know there was such a thing as "the prayers of the Church" until, as a Catholic, I began praying the Divine Office (actually only parts of it). At the front of the book of the Liturgy of the Hours that I purchased, there was a whole section devoted to explaining the difference between personal prayer and prayers of the church. You can find basically the same information in the EWTN library.
My Spanish-language Liturgy of the Hours book puts it this way (my translation):
'The purpose of the prayer of the Church is not the same as that of personal prayer, which is the conversation of a believer with God, but it is the dialog of the Church with her Spouse, of the people of God with their Father who has chosen them, of the community of those who have been sanctified by the blood of Christ with their Savior. This praying community is the Church in its fullest sense - the universal Church, the one who merits the title of "bride of Christ, radiant, without spot or blemish".'
To realize that throughout the entire world, literally millions of people each day are praying the same psalms and the same biblical passages, to know that the faithful have been praying in this same way for two thousand years, is truly wonderful (it fills me with wonder at the majesty of the unity that God calls us to). To know that people are not "reading" these psalms, these passages, but praying them (lectio divina) - and to take my place in this choir of prayer - is a taste of the eternal community of which we are participants. This is so much deeper and higher than the reading of the Bible in group Bible studies that I have been used to.
Not to say that group Bible studies aren't useful or important - they are - but they correspond more to the Bride reading a letter from her beloved, rather than participating in a conversation with Him. And of course, I'm not contrasting personal prayer or Bible reading with the prayer of the Church. All these are rich means of approaching God. I thank Him that He has provided multiple means of communing with Him, since not all who seek Him can read; not all can gather with other believers; not all have access to a Bible.
I know I have only touched the "hem of the outer garment" of the presence of Christ in the prayers of His spouse. I would love to hear from anyone who has been praying the Divine Office for long enough to give me further insight into this treasure of the Church.