Therefore God gave them up in the lusts of their hearts to impurity, to the dishonoring of their bodies among themselves, (ESV)
Mankind is prone to folly. As we have discovered in the previous verses in this chapter, God takes the first step toward mankind by revealing himself to his creation in the things that he has made. What is man's general response? Ignore God's existence. This ignoring of God leads to foolish thinking. What is God's response?
God gave them up in their lusts. Mankind thinks this is a good thing. It is not. This phrase, "gave them up" is a judicial term that basically means they are being turned over to their prison sentence. God walks away from them. This is a catastrophic situation. We know that God is the source of joy, life, light, and all goodness. When he walks away you are left with nothing good.
Where does man go after God gives him up? He chases after every impurity that his foolish heart can imagine. It is important to note that the lusts start in the heart. As the heart is corrupt with impurity it will direct the rest of the body to commit every kind of dishonorable behavior. Note that the remedy to this dreadful situation is a new heart, not restraints on behavior.
Mankind thinks that when he is engaged in all kinds of wickedness he is free. He is showing to the world around him that he can do whatever he wants with no worry about God restricting his behavior. The fact is every lustful decision secures the lock of man's prison cell. Man without God is trapped in total bondage to sin, lacking any kind of freedom.
If you are living a life without God I encourage you to cry out to him for forgiveness. He will break the chains you are bound in. If you belong to him have compassion on those who are in prisons of their own sinfulness. Introduce them to the Savior who died to free them.