Romans 8:24-25 meaning

In this passage, Paul is confirming that it is with hope that Christians, along with creation, eagerly await the time that our bodies are redeemed (v 23). For in hope we have been saved (v 24). 

When we see the word saved we should ask, "What is being delivered from what?" In this passage, believers are being delivered from the corruption of the Fall, but the deliverance hasn't happened in its entirety—yet. When we believe, we receive spiritual deliverance in the sight of God, with the Spirit as the first fruit. Through walking in the Spirit we can experience deliverance from the power of sin through a walk of faith daily, in opposition to the world. But our hope also looks forward to a time when our bodies and the entire earth will be redeemed as well, and no longer resists the will of God.

This hope is not seen: But hope that is seen is not hope; for who hopes for what he already sees (v 24)? If you already know the outcome of a sports game you can't hope that one team beats the other because you've already seen the outcome; you already know who will win and who will lose. 

Hope is not something that you can have if you already see the outcome. So, we as believers are waiting eagerly in perseverance for Jesus's return and His restoration of creation as though we see it: But if we hope for what we do not see, with perseverance we wait eagerly for it (v 25). 

Hebrews tells us that faith is believing in what cannot be seen as though we can see, and hoping for what we do not yet have as though we already possess it (Hebrews 11:1). It takes perseverance to continue in hope for what we do not see. 

Therefore, we should steadfastly walk in the Spirit and redeem the earth, in part, through a walk of faith. We have the privilege to do this until God restores it completely (vv 15-19). As we walk in faith, we are suffering as Jesus suffered, and laying up treasure in heaven.

This notion of walking in perseverance in the hope which we cannot see is restated by Paul in 2 Corinthians 5:6-8:

"Therefore we are always confident and know that as long as we are at home in the body we are away from the Lord. For we live by faith, not by sight. We are confident, I say, and would prefer to be away from the body and at home with the Lord."

As believers, we should live by faith, persevering and walking with the Spirit, while we wait (in hope) to be at home with God. Paul discusses this desire to be set apart from our sinful bodies at length in Chapter 7.