Daniel H. answered 10/08/19
Over fifteen years in Film & Video, Specializing in Post-Production
Some theaters still project in 16, 35 and 70mm, even for new releases, some even multiple projectors with IMAX screens. However, the traditional model for the last twenty or so years has been DCP (Digital Cinema Package). With this technology, a hard drive (or USB stick) is mailed to the theater. The film inside is encrypted with a license code which has a limited number of uses, so data on the number of times the film is shown and how many activations is sent back to the distributors. The encoding makes it somewhat difficult to rip the film directly from the hard disk or stick; from my understanding, it's encoded in a playlist XML format, so each 'chapter' (sort of like you see on DVD or Blu-Ray menus) plays in order and plays with a corresponding audio file, which all come from reference files.
Of course, this all goes right out the window when it comes to 3D technology, and some of the 4D cinemas now being set up (the ones where, on top of 3D, they rock your chairs back and forth, blow fans at you and completely immerse you in surround sound depending on what's happening in the film), as I have no idea how these kinds of things are programmed.
I know that distributors are also experimenting with cloud/satellite technology, which would allow the theater to directly download the film (or directly stream for live events), with a supplied license code. There are, of course, risks to putting the code and the film out online as opposed to keeping it localized to secure mail and physical media, but most signs point to distributors (and theaters) saving heaps of money doing it this way as standard sometime in the future.