I think the "snapshots" of the ciphertext at different times is referring to someone copying an encrypted file before & after it's been modified by you somehow, otherwise just copying an unmodified file twice should give you two identical copies.
If someone copies all your encrypted files one day, then comes back a week later after you've modified some files and copies them all again, they'll have two copies of the ciphertext.
I think the theory is that if they can see how the file is modified, it would give them some clue about how to modify the file themselves (maliciously). I don't think they'll be able to decrypt any files, but maybe modify some so they're not immediately noticed - they'd most likely appear to you (decrypted) as corrupted.
I'm not aware of all the potential risks, maybe eventually after seeing enough files modified it would give a clue about how to decrypt all the files, but I've never heard of that actually being done successfully, and I don't think there's any real risk of the files being decrypted from seeing two copies of ciphertext.
There would be a real risk of the non-encrypted (system) files being modified maliciously (to record keystrokes or store encryption keys, monitor all activity, etc) if someone has access to your computer, or even installing physical keyloggers or screen monitors if they have physical access. I'd say that's a far far greater threat than ever having EncFS decrypted.
