Cloud Atlas is a relatively simple movie disguised as a complex mess. The film, at its heart, is about little more than the everlasting vitality of life, and the unbreakable human will to survive.
But then there's the matter of the makeup, and that weird birthmark, and the intertwining storylines. Is that Ben Whishaw (Skyfall) under all that makeup? Or Hugo Weaving (The Hobbit)? How many Tom Hankses are there? If you split up the main characters into three groups, you'll see that each time period has a "Struggler," a "Villain," and a "Savior."
The Struggler in each story has a comet-shaped birthmark, which some have suggested indicates that all of these characters are reincarnations of the same "soul." Others have suggested that the common actors signifies some kind of spiritual connectivity. In reality, the interconnectivity of the characters has nothing to do with the actors playing them (though Weaving and Hugh Grant are pretty much only jerks).
The birthmark signifies a shared lust for freedom--a "birthright" to advance civilization, if you will--with all six stories paralleling each other pretty tightly (which is perhaps why the 45-minute climax was so utterly taxing). While some element of each plotline carried over to influence the next (Sixsmith, The Ghastly Ordeal of Timothy Cavendish, the Sonmi statue, etc.), ultimately the film does little to reinforce the theory that souls are being recycled.
Take a look at this infographic, which explains the character types for each time period, then check out our Cloud Atlas review.