I didn't understand what it would be about from watching the trailer, but it was intriguing so I downloaded it and gave it a go.
It takes place in the late 60's in Hong Kong, where Chow, the narrator, writes vivid and surreal fantasy stories. He takes room 2047 (next to room 2046) after seeing a woman, Su (Li Gong), in room 2046. He believes this place is where he, like others, can go to "lose memories" ("All memories are traces of tears", a title-card reads), which encourages him to start writing a sci-fi novel with the room's title. During his stay, he meets two women that affect him in different ways and he incorporates elements from his own life into his story "2046".
It may be a place, it may be a time, one simply doesn't know; but his story takes place in distant future.
In the writer's own life, he spends his days womanizing and writing successfully for a newspaper. As his life goes on, the story is more and more about his life. He writes as a form of release, since his life is empty and lonely.
This film is a splendid masterpiece that is about a writer who incorporates elements of his own life into his story. It is somewhat film noir, and reminded me of Cloud Atlas; except for the fact that it was more thought out and generally better.
One may wonder what the point of this poignant film is.
There are many interpretations, but the only way to find out is to see it for yourself. It is as riveting as Casablanca and jumbled and disordered as Pulp Fiction.