One accord praying is defined as conversational, agreement prayer. One accord prayer is praying "with" someone as opposed to "beside." The word "with" reveals a particular relation to while the word "beside" means near but not connected with. So praying "with" means you speak as one, agreeing in conversation, one subject at a time.
For an illustration of with and beside, imagine 4 moms, each with a cell phone. Two of these moms are "with" one another. The other two are "beside" each other.
From the two that are "with," there is a constant chiming sound almost drowning out the sound of the keys. But from the two that are "beside," there is only the sound of the keys.
The two that are "with" are having a conversation. It goes something like this:
Susan: Ann, will you pray for my son with me?
Susan: Dear Father, I ask that David will live a life worthy of the Lord and please You in every way, bearing fruit in every good work, growing in the knowledge of the Lord.
Ann: Yes, Father, I ask that David will conduct himself the way a Christian should, no matter how difficult the circumstances.
Susan: Lord, I agree, that David will not live one way at home and church, and another way at school. I ask that his Christian walk would be a part of every aspect of his life.
Ann: And Father, that you will open his eyes to what really pleases You, that he will know that obedience brings blessings.
That is one accord, conversational, agreement prayer. They are in "particular relation to."
The two that are "beside," however, have texts that read like this:
Mary: Dear Father, please help my daughter, Julie, to live a life worthy of the Lord and please You in every way, bearing fruit I every good work, growing in the knowledge of the Lord."
Kellie: Dear Father, please help my daughter, Kim, to live a life worthy of the Lord and please You in every way, bearing fruit I every good work, growing in the knowledge of the Lord."
No chiming sounds between them to say, "I hear you. I agree with you."
These two moms are "near but not connected." That is not an illustration of wrong prayer. But it is not an illustration of focused, one accord prayer, "agreeing together as directed and energized by the Holy Spirit." [Moms in Prayer International Booklet]
Did you notice that the moms who prayed "with" prayed differently? David's mom, Susan, prayed a scripture verse, Colossians 1:10 (NASB), for her child. Ann, then, agreed with Susan. However, Ann put the verse in her own words. She spoke from her own "box."
This is something we all do. We all pray from our own "box." Yet, the Holy Spirit is able to speak out loud in prayer to open up our "boxed" thinking through another mom's voice. If you think about it, this is similar to the way the four Gospels were written. Matthew, Mark, Luke, and John told the same story, inspired by the Holy Spirit, yet from their own "box."
Now, praying moms, which would you prefer?
With or beside?
As for me, praying with other moms for my children and for their children is much, much preferable.
Back in the city, they went to the room where they were staying—a second-floor room. This whole group devoted themselves to constant prayer with one accord: Peter, John, James, Andrew, Philip, Thomas, Bartholomew, Matthew, James (son of Alphaeus), Simon (the Zealot), Judas (son of James), a number of women including Mary (Jesus’ mother), and some of Jesus’ brothers.
Acts 1:13-14 (VOICE)