A combination of the words "shit" and "sabbatical." When you have to take a crap and you know it will take a while and you requires some form of entertainment while doing your business. When going "on shibbatical" one might take a laptop, telephone, book, homework assignment, magazine, gameboy, or perhaps a portable television.
"Hey John O, where are you going with your laptop?"
"Dude, I ate a shitload of taco bell earlier, I'm going on shibbatical."
The word regually spoken whilst shaking ones head, making ones cheeks wobble.
This word is usually used to describe obese individuals, or somethng crazy that made the user of the word laugh aloud.