Arrival times is just the time the ship is scheduled to dock at the pier or drop it's anchor.
If the ship docks at the pier, on most cruises you'll be able to depart the ship as soon as the gangway is in place.
If the ship drops anchor, you'll have to wait your turn to board the boats (tenders).
If the ship travels to or from another country -Fanning Island, Canada, or Mexico for example, you'll have to wait for US Customs to clear the ship before anyone departs the ship.
When a ship is scheduled to arrive, and when it actually arrives, doesn't have to be exact. A ship can arrive early or later.....