When you add a comment to a thread, it bumps the thread to the top of the list for that board. If you add 'sage' into the email (?) field, it will add the comment without bumping the thread. Each thread has an image post limit that will max out the thread and prevent the thread from bumping anymore (letting it slowly fall down the listing and eventually die).
So, using sage as a way to 'downvote' is just a way of adding towards the thread limit without bumping the thread. It's a round-about way to do it though (vs. direct downvoting).
"sage" originates from 2chan (aka Futaba Channel), which was the inspiration for 4chan. 'sage' is short for sageru.
iiuc sage comes from sageru which is a Japanese word meaning "lower." Its use is a polite way of saying "my comment is not important enough to bump the thread to the top of the page."
If this is true, sage can not be used to downvote at all, EXCEPT if there are enough sages to make the thread expire. However, that limit is something in the 100s. No one has the time and dedication to "sage a thread into non-existence," even though they sometimes call for it.
As was alluded to with "SAGE GOES IN EVERY FIELD," people hope to cause a snowball effect where others join in an sage the thread (by announcing loudly that they are sage-ing). In general, the idea of using sage as a downvote has been around for a while, even though it's anything but.
So, using sage as a way to 'downvote' is just a way of adding towards the thread limit without bumping the thread. It's a round-about way to do it though (vs. direct downvoting).
"sage" originates from 2chan (aka Futaba Channel), which was the inspiration for 4chan. 'sage' is short for sageru.
http://www.4chan.org/faq#sage
http://www.eudict.com/?lang=japeng&word=sageru