It's about the life of a young woman (and co-director and writer of the film), Marjane Satrapi, growing up in Iran during the revolution, and about the price one must pay for freedom. Sure, it does what it sets out to do and what is generically expected of a film of this subject matter, showing the (presumably Western) viewer that at the core the divide between our lives and that of those living in Iran isn't as great as it's perceived to be, and that we all crave the same basic things, but it does this in a genuinely innovative and moving way.
Persepolis takes a disorienting, complex event in history and makes it personal. The deaths, explosions, loss of dignity, loss of basic human rights -- we see each of these happen individually to members of Marjane's family, her friends, herself, and through that, both the impact and understanding of what happened is heightened.
It's a serious topic, but the filmmakers allow for the inclusion humor and lightness often as well, especially around the universal adolescent experience of rebellion. Despite the Western cultural ban in Iran, Marjane writes "Punk is not ded [sic]" on the back of her jacket and buys contraband Iron Maiden tapes, picking up her tennis racket and headbanging around her room.
The animated format packs a great and specific amount of detail into each frame, and also allows for an at times realistic and at times fantastical graphic focus on both Marjane's real life and what she imagines (chats with god and Bruce Lee-esque martial arts skills!). Using drawings instead of real shots enables Persepolis' creators to take a scary, overwhelming time and make it less difficult to watch as well as bring in a touch of whimsy where appropriate -- from simply a hand peeking out from rubble after a missile launch to jasmine flowers floating across the screen via Marjane's grandma's bra (yup).