There are two kingdoms at work in this world. There is the kingdom of darkness and the kingdom of light. Of course, the kingdom of light is the kingdom of God. The King of God's kingdom is our Lord Jesus Christ. The kingdom of darkness is this present evil age and the evil one. Satan and the powers of darkness are defeated when God's kingdom comes. Light defeats darkness every time.
God's kingdom is sovereign power and authority, ruling and reigning. God's kingdom is righteousness, peace, and joy in the Holy Spirit (Romans 14:17). God's kingdom is God's will. Simply stated, God's kingdom is God's sovereignty.
When God's people pray, "Your kingdom come," we are praying for the Holy Spirit to come to change people and situations in this present evil world. We are asking for God's will to be done. We are praying that the power of God will come with righteousness, joy, and peace in the lives of people through the King, our Lord Jesus Christ.
Jesus taught His disciples to pray the model prayer, also known as the Lord's Prayer. The focus of His teaching was on the kingdom of God, and that includes prayer. We should pray, "Your kingdom come, Your will be done on earth as it is in heaven." God's kingdom comes on earth in the power of the Holy Spirit to defeat the kingdom of evil.