Intercession - prayer on behalf of another. It naturally arises from the instinct of the human heart—not merely prompted by affection and interest, but recognizing that God’s relation to man is not merely individual, but social. (blueletterbible.org)
Anything we do on behalf of another, motivated by purely unselfish means, connects us to the heart of God. He designed us for a life on earth that is not merely individual in purpose, but social as well. Our ability to see others, love them, and act with kindness towards them, must be forefront in His design for us. After all, the greatest command is to "Love the Lord your God... and to Love your neighbor as yourself." (Matt 22:36-39)
Intercession is a word I only understand in the core of my being. Putting words to something grasped at the spirit level is a challenge. But the act of true intercession for another puts us at the closest to God's own heart for people as we will ever be. It is the act of praying on behalf of another whole-heartedly in the interests of God Himself, not merely prompted by our own selfish interests. When we are moved by the Spirit of God to intercede we are in our humblest, most unselfish, state. We are relying solely on the mercy of God for another human being. Crying out to Him as if we cared as much about this other person as we do about ourselves. We are in touch with God's heart, and we are powerful in prayer.
Being moved for a loved one who is broken to the point of despair, I find myself on my knees on the behalf of someone else. Crying out, as if it were my own heart that was broken because this person has no strength left to cry out. Perhaps this is one more way that God takes care of His broken children - by giving others strength for them. How comforting to know that God may one day take care of me in this way. That God has taken care of me like this in the past. Out of a power not my own, I am given God's heart, the clarity to ask for Majesty, Justice, Truth, and HOPE.
To pray for another with God's own heart is to glimpse a picture of God's initial intentions for us so long ago when He created the world in perfection. A glimpse of what our world will be like one day.
We do not know what we ought to pray for, but the Spirit himself intercedes for us with groans that words cannot express. Romans 8:26