Contemporary English Version (CEV)
As they say, the problem with living sacrifices is that they keep crawling off the altar.
These two verses are packed with meaning, and if you studied just these verses for a month, you would find no shortage of depth. In summary, Paul is calling us to live in such a way where we are giving ourselves completely to God, pouring ourselves out for his greater glory, willing to give up all we are for the honor of God. I don't know that we think like this very often -- it sounds challenging and costly, and we easily forget all that God has given us and only think about what it might cost us.
Paul goes on, telling us that God should change the way we think. If we are Christians, every thought should be captive to the will of God, so that we glorify him in all we do, honoring and praising him in public and private moments. It's all about God.
If we strive for this, we will find the life that truly is life, the abundant life that comes from God alone.