Church planter (and colleague of mine at Orchard Group) Jordan Rice on preaching that connects:
I would define contextualization as using the gospel to answer the questions that people actually have—to approach a text first seeking Biblical truth and a commitment to what God has revealed to us in scripture; then, answering the questions that people actually are asking in this present time.
Take, for example, a text about Jesus and the leper. It’s a great theological truth that Jesus became unclean so that we can become clean, or that Jesus would touch the untouchable. Those are great theological truths. But no one is asking questions about leprosy because it’s a foreign concept to us. Contextualizing that passage is answering the question, “What makes you feel unclean? What would make you feel like you’re not touchable, like God doesn’t want to come near you?”