If you're going to watch this (or have watched it), then you've definitely seen at least the first 15 episodes of the anime and the Book of Circus. It also wouldn't hurt to watch Book of Murder as well. If you haven't, I highly suggest watching that much (or just reading the manga) before watching this movie.
For those not following the manga or decided not to watch Book of Murder before this, seeing Snake with Ciel might be a little confusing. All the other characters (sans the movie-exclusive characters) I believe show up between episodes 1-15 of the first season and Book of Circus, so if you've at least seen that much then you shouldn't have any trouble following it.
Plot
Ciel and Sebastian (along with Snake) board a luxury cruiser which practically screams "Titanic parody" for two reasons. The first is for business on behalf of the queen, and the second is because Ciel is (secretly) worried about Elizabeth who is also going to be on the ship. His mission this time? To investigate a hospital cult which is trying to come up with a medicine to revive the dead.
Characters
The colorful cast is here, so I'm not going to go into specifics. The only character of note here would be Snake, as some people might be confused since I don't believe any of the animated stuff had him joining the Phantomhive group; this occurs in the manga just shortly after the Murders arc.
The other characters are still whom we've seen up until now; usually I'd list characters regardless, but if you're this far along in the series (and read my first couple paragraphs of the review) then you should at least have a handle on the basic cast.
Music & Animation
The music is haunting in just the right places, and the ending song fits with the mood; I have no complaints about that.
The biggest problem this movie has is in its animation. The CGI used to animate nobles and various other characters moving in the background is laughably awkward at times, even during scenes which aren't supposed to be laughed at. Thankfully, there's usually something in the foreground worth paying attention to, but that still doesn't excuse the poor job with the CGI.
Overall
Expect some Titanic references and jokes; if you didn't figure out the first time you saw the ship that it was parodying the Titanic...well, it's fairly obvious.
A minor nitpick (more of a personal one) with the animiation is the amount of blood in the movie. It's Black Butler so of course it's going to be bloody, but this went above and beyond into the "gore" category.
I am not a fan of gore. At all.
It's the main reason I stopped watching Attack on Titan, and I actually grimaced and closed my eyes a few times in this movie. Fans of blood and gore, you'll love this. If you aren't fond of geisers of blood and even the occasional organ spewing forth, then proceed with caution (if you wish to watch it).
I'd certainly recommend watching it. I haven't read the arc in the manga (wanted to see the movie first since I enjoyed the other animations for Black Butler), so I don't know if there's as much gore there. There's always a certain amount of blood in this series (it's freaking Black Butler; it's going to have blood, that's a given), but this movie really pushed that. In fact, I feel they went a little overboard with the amount of blood at times.
Again, I'd still suggest watching it...just be prepared if you're not a fan of it.
I actually don't have many nitpicks or other issues with the movie, which I usually put here in the "overall" section since I use it for personal opinion. I had a lot of questions about certain aspects, but all of them were answered during the big reveal with the antagonist.
The twist at the climax...I was totally not expecting. I typically say that it's hard to "get the jump" on me when it comes to anime/manga, because I've been watching and reading it since the 90's; I've seen so many tropes and cliches, so for this to come out and surprise me...
Well, that increased my enjoyment because I didn't see it coming. People who read this arc in the manga first will obviously know what's going to happen, but I didn't, and I'm glad I didn't read that arc yet.
All in all, the movie is excellent. The pacing is great, the characters are themselves (with a couple surprises, even), and the twist is unexpected. We even get treated to some past history between Sebastian and Ciel, which I'd been wondering about for a while.
I'd love to give this movie/arc a 10/10 (a rarity for me), but the CGI honestly ruined it. Since it also doesn't cover a couple things leading up to the arc (such as Snake joining the Phantomhive group), I had to dock a little off of the story since this is in movie format...and anyone who watches the anime should know these things (not just those who reads the manga).
Otherwise, this competes as my favorite arc with the Book of Circus. A solid arc/movie.