The Partial Inscription Reads  (conjectural letters in brackets):
[DIS AUGUSTI]S TIBERIÉUM
[...PO]NTIUS PILATUS
[...PRAEF]ECTUS IUDA[EA]E
[...FECIT D]E[DICAVIT]

The translation from Latin to English 
To the Divine Augusti [this] Tiberieum
...Pontius Pilate
...prefect of Judea
...has dedicated [this]

It was at Caesarea where Paul was tried before Felix and later Festus and King Aggrippa. He remained imprisoned here at least 2 years and wrote several epistles. Acts 24-26
Philip, the evangelist and one of the seven, later settled here. Paul and his company stayed with him before he was arrested in Jerusalem. Acts 21:8

​Discovered at the city of Caesarea in June 1961 by archaeologists team of Dr. Antonio Frova near the area of an ancient theater built by Herod the Great around 22-10 B.C. It’s original use was to the dedication of a temple to Tiberius. However, the stone was then reused in the 4th century as a building block for a set of stairs belonging to a structure erected behind the stage house of the Herodian theatre. When it was discovered it was still attached to the ancient staircase, by the archaeologists. This is an irony of sorts of Pilate becoming a mere footnote in history. Some scholars were beginning to question if a Pontus Pilate had ever been governor of Judea. The only references outside the Gospel accounts are by Tacitus and Jospheus.

Caesarea Maritima was founded by Herod in 22-10/9 BC on the Judean coast of Galilee.  The city and harbor were named after the emperor Caesar Augustus, Herod’s patron in Rome. Herod built a temple which he dedicated to Rome and Augustus, a theater, and an amphitheater, as well as a royal palace - basileia.
The Harbor was an enormous feat of ancient engineering with many quays and anchorage spots. It was constructed of huge stones, including materials imported from Italy, using Roman hydraulic cement technology which experts are still studying today.
Fresh water was carried in by an aqueduct provided water for the palace, public baths, fountains and elite land owners.
After Herod’s death in 4 B.C. it became the provincial capital of Pontius Pilate, Felix and Festus.