The relationship of brothers is a reminder that such belong to the same family, the family of God. This is the basis of meaningful intercessory prayer because we pray to the heavenly Father on behalf of other members of his family. Indeed it is not possible to show brotherly love without such prayer. The proof that we love one another is that we bring one another to the Father in our prayers. This is what the apostle Paul did with regard to the Christians that he knew about, as we can see from his letters. He prayed repeatedly for believers all over the known world.
Obviously we can imagine someone praying in a clinical manner, merely mentioning people by name but not getting involved in praying in a deep manner for them. That is where the other details mentioned here prove helpful. True prayer requires right thinking and Peter mentions two aspects of such thinking here. The first is that there has to be unity of mind and the second is that there has to be humility of mind. Unity of mind could include agreement about the beliefs that are held. It could also include agreement about what we should be praying about. Another word for this is harmony.
At the same time, there has to be humility as we pray. Pride is obnoxious anywhere, but the worst place for it to show itself is during corporate prayer. Imagine thinking that our petitions are better than those of others merely because we use better words or frame our requests in accurate theological language. Of course, it is important to have accurate terminology, but our awareness of them should be a matter of gratitude, not pride. After all, our prayers remain powerless without God’s input; we require divine wisdom as to how and when we should pray the requests on our minds.
Humility shows itself by a willingness to ask other people to pray for needs and burdens we have; pride stops us from making such requests. There are some petitions that God will not answer until you ask others to pray about them as well. Harmony and humility are essential features of true prayer.