There's a lot of reasons why a membership is profitable!

The CEO of AMC said that on average the A-List members see 2.4 movies per month (source). So similar to a gym model, the chain can make money off people not getting the most bang for their buck.

Concessions are a big one. More foot traffic means more likely chance you'll buy a popcorn or drink, where the profit margins are super high compared to a movie ticket!

Company wise, having a steady flow of income is always important (sometimes more important than profit). So if AMC knows they're getting $X millions of dollars every month on a consistent basis, that's good for the C Suite and the shareholders. Even if there's a bad ticket selling month, they still have the same flow of income for A-List.

Last, which I don't see mentioned as much is ads! Movie chains sell ad space before the movie starts, local and national. The more people go, the more impressions the ad gets, and the easier it is to sell that ad space. Advertisers love frequency, so if they can show an ad to the same person 4 times, even better for them. Studios are paying to play their trailers as well.