"The last thing on earth" requires a context, as the first replier indicated. However, to answer your question more generally, what it means is that if there were no other choice available, none at all, that you still would not take the option offered.
So, "I wouldn't eat that potato, if it were the last thing on earth left to eat. I'd go hungry first."
The potato is so unappealing, that I would not touch it, even if it meant starving to death.