Beyond the Black Rainbow is a 'head film' in the tradition of films like Jodorowsky's and El Topo, or David Lynch's Eraserhead. It forsakes traditional narrative and character development for a more abstract experience whose central goal is to immerse you in a specific mindset, rather than tell you a story. In that respect, it's a great success, but it also means the film isn't for everyone.
The basic plot of the film involves a scientist experimenting on a girl who may or may not have some kind of supernatural psychic ability, and it all takes place in an alternative future version of 1983. But the narrative is only a device to get you in the headspace the film wants to create.
Film is traditionally used as a narrative medium, but seeing a film like this reminds you that it can be so much more. It's not limited to telling stories in the typical Hollywood glamour, it can be a more abstract and trippy experience.
I imagine a lot of people are going to be watching this movie under the influence, but to me, the film itself provided an altered state. If you surrender to the images and soundscape of the film, it will evoke things in your mind. It's the kind of film that presents images and allows you to come to your own conclusions about what exactly they mean and drift off from there.
Ultimately, you probably can already tell if this film is for you. If you loved the last 30 minutes of 2001: A Space Odyssey, see this now. If you thought that movie was boring because nothing happened, skip it. Beyond the Black Rainbow is a film that knows its audience, and speaks to them in a way that few films do. It's a perfect movie, but I'm really happy it exists.