During the first century, the city of Caesarea was the Roman administrative capital for the entire region. King Herod constructed the second largest port in the world at Caesarea. It consisted of two "ports". The outer port is where many of the larger ships would be docked. Transportation to the outer port would take place via smaller boats which were docked in the inner port.
The steps in this picture are from the inner port dock at Caesarea. During the first century, travelers would have used these steps to climb down from the dock to enter a small ship. This small ship would transport them to the outer dock where the larger ship would be located.
After the apostle Paul used his privilege as a Roman citizen to appeal his case to Caesar, he was loaded onto a ship and sent to Rome. It is possible that Paul used these exact steps as he left the city of Caesarea for the final time.