Long before there were Christians, Jews prayed every morning and every evening in the village synagogue as a community. They read from the Bible and prayed. When the Christians were thrown out of the synagogue, they continued to gather together to pray. They added New Testament readings and prayed in the Name of Jesus. But they prayed in the same way. This ancient pattern of Bible study and prayer is often associated with monastic houses, but it is the heritage of all Christians. And it was Thomas Cranmer's reformation which restored it to all Christians. Cranmer eliminated the monastic midnight office of Vigils and put its long Bible readings back into Morning and Evening Prayer. This kept God's Word always in our mind. It ensured that those who use the office don't fall for so many tricks of The enemy because they know the Word. of God and recognize that which contradicts it. The Word of God becomes what they think of and meditate on in prayer, rather than any particular devotion like the rosary. Recitation of the daily office, along with weekly Eucharist and meditation and reflection on the readings in the daily offices of Morning and Evening Prayer became the distinguishing feature of English or Anglican spirituality.
One interesting feature of Divine Office is that it is intended to be sung in community. King David composed the music for the psalms, and variations of that music--plainsong--have been applied to the other parts of the office, as well. All music stimulates the brain, but David's music is said to be particularly healing and stimulates those areas of the brain which help us connect with God, much as incense does. And music brings joy. It is just about impossible to praise God in song and be gloomy at the same time!
The offices are meant to be offices of praise of God. By praising God, we draw into His presence, we go online with Him so we become more aware of His promptings and counsel throughout the day. His presence is powerful, and The enemy flees it. Sometimes our more charismatic friends speak of an open heaven brought about by praise--a state of affairs where there is no demonic barrier to prayers being answered.
Like all prayer, the office is most powerful when one pays attention to God as one prays, that is resists the wandering of the mind. We do this intentionally to better worship and honor God. However, this means it is better to pray only one office or a shorter version of the office than to drone on with one's mind and heart far away.
As you can see, when one prays the office, one brings down the Presence of God and sends the devil scurrying and this alone benefits all of the church and humanity. The office also has time for intercessions, that is direct prayer for others.
Today it is easy to be sucked into technology, run ragged, or cut off from community and fun. Singing the office brings joy, Scripture, and common prayer into our days.