If you don't know what Black Swan is, let me tell you. It is the story of a young woman who has the dream of becoming the lead in the ballet. This honor is eventually granted to her. She plays the Swan Queen in Tchaikovsky's Swan Lake. She practices. She performs. Now that is the top level exactly what happens story. That's not the interesting part.
To put it bluntly, the thing that I really appreciate about this film is the dynamic lead role played by Natalie Portman. We see this young woman that society might call uptight, or perfect. We see her mind and body go through such a dramatic change through this film that you can't help but feel an emotional connection to her. You are taken on this journey; no longer a spectator.
Something that I found to be one of the most engaging tools used is the fact that this film follows the libretto of Swan Lake perfectly. It's just modernized. It's very meta. A telling of Swan Lake about Ballerinas fighting for the role of the Swan Queen in a performance of Swan Lake. It's so meta that I feel like Dan Harmon came up with the idea. But seriously, read the synopsis of the libretto and then watch the film. I want to do an in depth analysis and comparison of this, but I feel like that might bore you, so I will just move on and provide a link the the synopsis at the bottom.
The music in the film is amazing as well, but I don't know what else you would expect when the source material is Tchaikovsky! I guess what I should be saying is the selections were perfect. This score does exactly what it's supposed to do. Accompany the film and complement the story by almost becoming one of the characters in the film, and that's what this score does. The music grows and transforms along with the Natalie Portman. And lastly, the choreography. I am in no way a ballet expert, but I have watched a few ballets and appreciate good choreography, and this is incredibly well done (if you're looking for a really good ballet, look up The Rite of Spring Nijinsky Choreography. That's my favorite).
I guess if I want to boil it down, It's a beautiful movie, with beautiful acting, beautiful sets, beautiful costumes, beautiful music, and a beautiful story. Watch it and enjoy it.