Robert Wiene's The Cabinet of Dr. Caligari is considered, along with F. W. Murnau's Nosferatu, one of the key films of the German Expressionist movement of the 1920s. The films produced during this moment were highly influential to horror as a genre, with later films utilizing German Expressionism's unique production design and lighting. Indeed, production design is one of the key elements of The Cabinet of Dr. Caligari, with the entire film taking place in a very angular world.
As a film made relatively early in the history of cinema, The Cabinet of Dr. Caligari has a structure more akin to a play. The story of the film is told in six acts and the surreal world of the film looks very much like a set on the stage. However, the film also utilizes some very cinematic elements, such as the use of shadows and a scene where giant words appear around a character. Some people, such as Roger Ebert, considered The Cabinet of Dr. Caligari to be the first proper horror film. However, I would argue that the film is a different kind of horror than the films that would arrive later.
If there is something that helps The Cabinet of Dr. Caligari work as a horror film is the use of garish make-up on the characters, particularly the somnambulist Cesare. It can be safe to say that Cesare, characterized by dark circles around his eyes, provided a template for "living dead" characters that would appear in the years to come. Apparently the revelation of Cesare was a source of fright for many in the audience, though the effect isn't quite the same watching the film on a TV screen.
Undoubtedly, The Cabinet of Dr. Caligari is a very influential film, even though it is ultimately more about its production design and lighting more than the story itself. Personally, when it comes to films from the German Expressionist era, I'll probably be quicker to revisit Nosferatu or Fritz Lang's Metropolis than this film.