Remember back in chapter one Paul spoke of the resurrection power that God used to raise His Son, Jesus, from the dead, 1:19,20. It is this same power that God is using to build up our inner strength. And He is drawing from all His glorious and unlimited resources He has at His disposal to accomplish this through the indwelling Holy Spirit!
One of the things I like to say is that it is impossible for any human to live the Christian life in their own strength. They need the power of God working in their lives to "demonstrate their salvation" (Philippians 2:12) before a watching world. The believers real power is not their outward strength or their own inner fortitude to try to live like a Christian. The believers real power comes from their surrendered life to Jesus Christ, relying on God to empower them to live for Christ. Paul knew this in his own life; Note Philippians 3:10. And that's why Paul is praying for this to happen in each believer's life.
Remember, Paul is drawing from his own experiences in Christ to know how to pray for others. Are you praying this request for your Christian friends, your believing family members, your pastor and your missionaries? Are you praying this request for yourself?