Intercessory prayer is a specific type of prayer.
I am not a teacher, so I will put the responsibility of learning on the reader. I am more than open to dialog on any of these topics. I’m sure that I will be too academic for some and will have many places that will be further explanation in order to truthfully express what I’m trying to say.

Let’s look at some definitions:

From Merriam-Webster’s Collegiate Dictionary (on-line at dictionary.com)

Main Entry: in·ter·cede
Pronunciation: "in-t&r-'sEd
Date: 1597 : to intervene between parties with a view to reconciling differences : MEDIATE synonym see INTERPOSE

Main Entry: in·ter·vene
Pronunciation: "in-t&r-'vEn
1 : to occur, fall, or come between points of time or events
2 : to enter or appear as an irrelevant or extraneous feature or circumstance
3 : to come in or between by way of hindrance or modification
4 : to occur or lie between two things
5 a : to become a third party to a legal proceeding begun by others for the protection of an alleged interest b : to interfere usually by force or threat of force in another nation's internal affairs especially to compel or prevent an action synonym see INTERPOSE

Main Entry: in·ter·pose
Pronunciation: "in-t&r-'pOz
1 a : to place in an intervening position b : to put (oneself) between : INTRUDE
2 : to put forth by way of interference or intervention
3 : to introduce or throw in between the parts of a conversation or argument
intransitive senses
1 : to be or come between
2 : to step in between parties at variance : INTERVENE
3 : INTERRUPT
- in·ter·pos·er noun
synonyms INTERPOSE, INTERFERE, INTERVENE, MEDIATE, INTERCEDE mean to come or go between. INTERPOSE often implies no more than this . INTERFERE implies hindering . INTERVENE may imply an occurring in space or time between two things or a stepping in to stop a conflict . MEDIATE implies intervening between hostile factions . INTERCEDE implies acting for an offender in begging mercy or forgiveness .

What does it mean to intercede? According to Webster, intercede means to go or pass between and the word implies acting for an offender in begging for mercy or forgiveness; to intervene between parties with a view to reconciling differences.
Another definition of the word intervene means to become a third party to a legal proceeding begun by others for the protection of an alleged interest.
When we begin discussing intercessory prayer we have to first remember that Jesus did the intercession once and for all. By all rights, God the father has condemned us. We are guilty of sin and deserve death. But Jesus INTERCEDED and paid the price for the sins of the world. By His death, burial and resurrection, he came between us and the law of God and bought redemption with his own blood.
He continues his intercession and is our mediator. The book of James states that “there is one mediator between God and man, the man Christ Jesus.” John 1:18 states:
“No one has seen God at any time; the only begotten God who is in the bosom of the Father, He has explained Him.”
”Jesus declares to us what God is like.
When we pray in an intercessory manner we are acting on behalf of that intercession. Thus, we are praying in Jesus name or on His behalf!

Dutch Sheets ( http://www.dutchsheets.org) in his book Intercessory Prayer describes it this way:

You have probably heard of the small child who “was drawing a picture and his teacher said, ‘That ‘s an interesting picture. Tell me about it.’
‘It’s a picture of God.’
‘But nobody knows what God looks like.’
‘They will when I get done.’ Said the young artist.
Jesus came and drew us a picture of God! Now we know what He looks like.
But that’s not the only direction of His interceding. Great irony exists in the fact that Man who was meant to be God’s intercessor, mediator or representative on earth now needed someone to mediate for him. He who was made to represent God on earth now needed someone to represent him to God. Christ, of course, became that representative, intercessor or mediator. Not only did He represent God to man, but He also represented man to God. This God-man was the attorney for both sides!
He is the ultimate, final and only go-between. He is “ the Apostle [God to the human race] and High Priest [ the human race to God] of our confession” (Heb 3:1) He is Job’s great go-between, hanging between heaven and earth placing one hand on God and the other on humans (see Job 9:32,33)”


1 Tim. 2:5) Dutch Sheets continue’s to explain that Christ is our representative to guarentee our access to the Father so that when we ask ( John 16:26) that He is not doing our asking or petitioning of the Father for us: “In that day you will ask in my name, and I do not say to you that I will request the Father on your behalf.”

Christ is mediating our redemption so that we can do the asking!

The Father accepts us for one reason – because Jesus died on the cross, was buried and rose again for our sins. When we ask something on Christ’s behalf, when we ask in Jesus’ name we are asking for credit on the basis of the very being of Christ and His meaning to the Father.

So if Christ has done the work, why should we pray? Why should be intercede in prayer? Basically, the answer to that is: because Jesus tells us to. He commands us to pray for one another so that we may be healed. (James 5:16)
Therefore, confess your sins to one another, and pray for one another so that you may be healed. The effective prayer of a righteous man can accomplish much.)

Another answer is because God has chosen to work through the prayers of his people. We are given the privilege and the responsibility of coming to the throne of grace.
God wants us to represent our brothers and sisters in Christ before the father. He wants us to learn to be Christ like.

So intercessory prayer is meeting with God in ‘Jesus name’ and on behalf of another human being. Our job is not to INTERCEDE, MEDIATE, RECONCILE OR DELIVER. Our job is to distribute and release Christ’s intercession (mediation, reconciliation and deliverance)!

We can have power in our prayers because we are representing what Christ has already done. We can be bold in asking for answers from God the father because the price has already been paid.

Our authority comes from being called to represent Christ’s work of intercession. As long as we function in that capacity, we function in Christ’s authority. We’re not doing our works, He is doing his works through our prayers.