Around 2:00 - 2:30 Central time the Captain announced "Man overboard" and instructed the crew to their appropriate stations. The ship begain to slow down but of course it takes a long time to stop a ship this size. Sometime later we heard a page for a passenger. Then a bit later the Captain came on again to update us - he said that several passengers had witnessed someone going overboard.
Then around 3:30 - 4:00 maybe (I may be off there) all passengers were ordered to their cabins so that they could check to be sure who was here.
I later saw from my balcony a low flying prop plane (I think it was the US Coast Guard but I was looking into the sun and I'm not sure) circling a couple of times and more activity from the Princess rescue craft as we pretty much just stayed in one spot, occasionally rotating in place. Finally around 6:00 the Captain announced the sad news that the body had been recovered.
One passenger said that they "heard" the person had been climbing on the rail, and while that is very believable, I have no idea if that is accurate or not.
The person was traveling with at least one other person, and I can't imagine how they must be feeling right now.
For those curious, the Captain announced we would be arriving at our next port of call (Grand Cayman) as scheduled.
If I hear anything else, I'll update this post at that point - maybe some other people who saw more will be able to add more details.