On the surface, they serve decently good food and an array of cocktails and other beverages, and it generally isn't overpriced. They have great milkshakes and they'll bring you warm cookies just as soon as a giant bowl of popcorn with parmesan.
But that stuff isn't strictly unique anymore; there are other dinner-and-movie chains.
What really makes them special is all their auxiliary stuff. Before a movie, instead of ads they show relevant obscure video clips that are funny and/or interesting. Before a superhero movie they might show relevant action figure commercials from the 80s, or clips of goofy unlicensed knockoff movies that they found on YouTube, etc. Famously, you're not allowed to talk/text once a movie is playing [1]. They'll have themed cocktails and food for movies that are currently showing. Every month they pick a selection of classic movies and do showings of those throughout. Sometimes they'll bring in an actor or the director for after-screening Q&A. For cult hits they'll do themed "movie parties" where everybody's encouraged to quote/sing-along, and often there are props. We went to a Monty Python and the Holy Grail party where everyone was given, among other things, coconut shells to clap. We saw Hackers on the big screen (which was incredible in its own right), and everyone was encouraged to wear their best hacker-punk getups and then they had a costume contest (and we got to take home floppy disks with "HACK THE PLANET" emblazoned on them). We saw Akira on the big screen (!!) and they had a synchronized laser-lightshow in the theater. We went to an "anime brunch" they did several Sunday mornings in a row where they'd pick a genre of anime and show four or five episodes from different shows and you could order coffee and stuff and it only cost $5 at the door.
And the person hosting/organizing these events always comes up to the front and talks about the thing you're going to be watching. They're personally invested. They geek out, telling anecdotes from their own life and giving background on why people love this thing so much. It gets you excited even if you've never heard of it before.
Everything - even the decorations and marketing - gives you the distinct sense that everyone calling the shots at this company is super into movies, and their enthusiasm is contagious even if you don't consider yourself an enthusiast
[1] Except at movie-parties, which are all about audience participation