Spirit Fm says this was a “float-by” similar to that of military jets doing a fly-by:

And Clarence Mitchell, who is representing Costa Cruises, said: “Mr Foschi confirmed the captain had been approaching the island of Giglio to ‘make a salute’.

The Guardian likewise has this nugget:

Foschi said Costa’s ships had their routes programmed, with alarms sounding when they went off course. “This route was put in correctly,” he said. “The fact that it left from this course is due solely to a manoeuvre by the commander that was unapproved, unauthorised and unknown to Costa.”

Though the company would provide Schettino with all necessary assistance, he said: “We need to acknowledge the facts, and we cannot deny human error.”

Foschi said Schettino was highly skilled, with all relevant qualifications, and that the liner had passed recent safety checks. But his remarks will be seen as confirmation of reports that the ship was making an unofficial sail-by of the island.

Yahoo News sums it all up:

At a news conference today, Costa Cruises Chief Executive Officer Pier Luigi Foschi said the ship’s captain, Francesco Schettino, made an unapproved, unauthorized maneuver to change the ship’s programmed course. Italian media has reported that Schettino was close to the shore in order to wave to a friend who was on land.