When we pray for God's Kingdom to come we are aligning our hearts and lives around his just and righteous rule and reign in the universe and his authority in our lives. When the Old Testament prophets spoke about this they described God's rule in seven primary ways:
Righteousness & Justice
God’s Manifest Presence
Return from Exile
Jesus is saying, "I want you to pray for the rule and the reign of God to break out into the world around you. In your neighborhoods. In your homes. In your relationships. In all your situations!" And when it does you will see people being set free from that which is enslaving them. You will see righteousness and justice being established. You will see the ceasing of conflict and the restoration of peace. You will see a sense of great joy in life. There will be a sense of God’s manifest presence. You will see healing - souls, emotions, physical bodies. And there will be sense that the people of God have come home. They have finally found their place as God’s people in the world.
These are the things that we are to be praying for and seeking in our world. These are the things that we are to be calling down into our situations
In other words, prayer is not only about conversing with God, prayer is about collaborating with His actions in the world.
The apostle Paul said we are “God’s fellow workers” We are co-laborers with Christ. So when we see poverty and disease, the lack of justice, hostility and hatred we are to bring these things to God and ask that all of these situations would be transformed. That the rule and reign of God would break in.
Prayer is seeking to weave the Kingdom of God into a fallen world.