Celebrity Reflection was a 'repositioning cruise'.  Some cruise lines shift their fleets from winter cruising to summer cruising, and when they do, they will move all their boats, one by one, from (in this case) the Carribean to the Mediterranean or nearby waters.  In the fall, the entire fleet returns to its winter cruising ports.  Since the ships are making a one-way trip and not returning for half a year, passengers either fly in to the origin port and take the cruise home, or they fly home after the cruise.  The cruise lines typically offer cut-rate fares for both the cruise and the flight so that they fill all the staterooms.

The one other option is to tour Europe for 6 months and take a fall repositioning cruise home when the fleet repositions.

Transatlantic (trans-anything, really) cruises involve many 'sea days' when the only thing visible from the ship is 360° of horizon.  Passengers may spend their days sunning themselves on the pool deck, or using the pool or hot tub, or indulging themselves at the spa.  There are also seminars and presentations, usually in the ship's theater during the day, often related to any of the ship's destinations.

Since this ship was destined for Rome, what better than a history of the Roman Empire.