Based upon Catechism paragraphs 2634-36:
Intercession derives from the Latin for “go between,” with the sense of intervening on behalf of someone. As the root word suggests, intercession is a form of prayer in which we ask God to help others, offering Him our petitions for their sake.
Intercessory prayer is an act of love, for we are truly seeking the good of others by praying to God on their behalf. In so doing, we exhibit a “heart attuned to God’s mercy.”
More astonishingly, we are thereby caught up in the mystery of God’s own life, where intercessory prayer wells up within the depths of the Most Holy Trinity. Jesus, the Eternal Son of God, continuously prays to the Father for us, as does the Holy Spirit. We enter into this dynamic of divine mercy whenever we pray for others, and especially when we pray for our enemies, as Jesus taught us.
Most often, however, our intercessory prayer will involve those closest to us, as we beg the Lord for the needs of our families, friends, neighbors, fellow members of the Body of Christ. We may even feel our faith stretched if our intercession doesn’t seem to help, if changes don’t occur for the better.
But in these difficulties, we must remember that God always respects the freedom of others. Our petition may require a certain level of openness or receptivity on another’s part, and if that person is not ready at a given point, the Lord will not force the issue. Rather, He will offer His grace according to His inexhaustible patience with us.
For that reason, we should never give up praying for someone, no matter how impossible the case may seem. God may be moving us to pray, so that He will cause it to bear fruit when the time is ripe.