It means "a society governed by its worst citizens," which applies particularly well to this society and pretty-schmucking-well to every other society I can think of. "Kakistocracy" also brings to mind soundalikes I just made up like "khaki-ocracy" and "caca-ocracy"--societies governed by khaki-wearers and fecal matter respectively.
"-ocracy" has spawned a bunch of words not involving shit, pants, or bad citizens, including these I just found on Google:
Personally, I'd rather live in a canoli-ocracy or a Jamaican-jerk-chicken-wing-ocracy. Or maybe a penguin-ocracy--just because they're cute.