In his sermon, Pastor Cody Harmon discusses the metaphor of new wine and old wineskins from Luke chapter 5. He emphasizes the need to let go of old ways of thinking and living in order to make space for God to work in our lives. Pastor Cody encourages listeners to seek guidance from Jesus and be open to new seasons with Him. Ultimately, he reassures that God is faithful and desires to bring about something better in their lives.