It's complicated.
First, it's 1850 & this guy Ewing is in the New World, writing a journal. There's slavery & a possible murder plot. Halfway through, it abruptly changed to:
1936, where a composer named Frobisher is reading Ewings journal, while composing a piece called cloud Atlas. frobishers lover is a guy named Sixsmith, & then the plot jumps to:
1970, where a journalist named Luisa Rey meets old man Sixsmith, who's a physicist & tells her about a conspiracy & just when it's getting dangerous, it jumps to
2012 & it turns out the whole Luisa Rey story is a mystery being read by a guy named Tim cavendish. Cavendish ends up accidentally committing himself to a nursing home (he thinks it's a hotel) & he's trying to escape and then:
2140 dystopian future Korea, a replicant named Sonmi escapes from her fast food slave job & watches "the ordeal of Timothy cavendish" a famous old movie , & then
2300 Hawaii after an apocalypse, the people worship Sonmi, their holy work is a recording of her confession to a crime back in NeoKorea.
And then the whole thing goes backwards back to the beginning, so you get to see how all the stories ended.