There are many fruits of prayer, and a primary one is its ability to bring us into communion with God and even with other people.
The Catechism of the Catholic Church explains this aspect of prayer in the following paragraph:
In the New Covenant, prayer is the living relationship of the children of God with their Father who is good beyond measure, with his Son Jesus Christ and with the Holy Spirit. The grace of the Kingdom is "the union of the entire holy and royal Trinity . . . with the whole human spirit." Thus, the life of prayer is the habit of being in the presence of the thrice-holy God and in communion with him.
Every time we pray, we are placing ourselves in the presence of God and seek communion with him.
We may not always recognize or feel this union with God, but it a fruit of prayer that is made possible through our baptism:
This communion of life is always possible because, through Baptism, we have already been united with Christ.
Our baptism put us into a covenant relationship with God, a relationship that we can foster through prayer.
Not only can prayer unite us with God, but it can also unite us to other people:
Prayer is Christian insofar as it is communion with Christ and extends throughout the Church, which is his Body. Its dimensions are those of Christ's love.
Whenever we pray in union with Christ, we are praying also in union with the Church. We are all members of his Body and that very fact unites us in a mystical way.
The next time you make time for prayer, open your heart to God and let his presence fill your soul with peace.