Our passage today is a little technical, but it gives us a good doctrinal overview of creation, the fall, redemption and eschatology!!! ("Escha-what?" - don't worry - all will be revealed.)
Paul is addressing the "elephant in the room". Creation was originally perfect, but not any more. It's broken. There's suffering—terrible suffering—in our world. Creation wasn't made that way, but it was "subjected to frustration".
When God created the universe and placed humanity at the apex of creation, He gave humanity a choice—He gave us free will. By doing this, He created a space wherein we had options and with those options came consequences. The rebellious choice of humanity, embodied in Adam and Eve, led to consequences (which are allowed by the Creator and lead to the frustration of the earth - we call this "the Fall.")
Paul describes the consequences of the Fall as our "bondage to decay." If you read Genesis 3 you'll see how four relationships were broken when Adam and Eve sinned:
We are still experiencing the pain of these broken relationships.
But the "subjection to frustration" didn't come without a counter-plan. Although we disowned ourselves as God's children, His plan is for us to belong to Him again - His plan is adoption and redemption. Redemption is a technical term used to describe being bought out of slavery. When creation is "subjected to frustration" God plans to adopt us and make us and creation His own again. This is what eschatology is all about - the ultimate plan that God has to restore our broken world.
So today's passage is a beautiful overview to help us understand when we see the incredible beauty and potential of Creation, but are frustrated by the pain we see in the world. The earthquakes, famines and tsunamis of our world are the groans of brokenness, but the time has come (and is still unfolding) when we will be restored and creation will be liberated too! And when that happens it will be a glorious day!