Acts 28:8

And it came to pass, that the father of Publius lay sick of a fever and of a bloody flux: to whom Paul entered in, and prayed, and laid his hands on him, and healed him.

The healing took place during Paul's stay on Melita. Paul entered in to the father of Publius, who lay seriously sick with fever and bloody flux, and prayed for him and laid his hands on him, and he was healed. The Lord worked through Paul and his fellow laborers in this healing. After this healing, others on the island who were sick came to be healed.

The healing shows that God had a special purpose in Paul's sea journey to Rome as a prisoner. Though bound, Paul's work went forward and his bonds spread the knowledge of Christ. The healing was one of the miracles God worked through Paul so that the ship's crew would witness God's power through him and the heathen would hear the name of Jesus. Many were converted through Paul's teaching and by witnessing his miracles.