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1.
When you gotta take a big shit, and you drop it all in one steamy log, rather than many shits. Its glorious and sought after by many cultures. Some say it's where the term "holy shit" derives from. A one-logger must be chosen by God, and cannot be artificially induced, thus banning the faux-logger.
ex 1)

Guy1: hey man, i just dropped a one-logger!
Guy2: HOLY SHIT dude no way, u snap any pics?
Guy1: OFC, wanna see?
Guy2: Ive never seen anything so glorious.. what was it like..

ex2) the tweet:
Yo twitter, i just dropped a one-logger. #YOLO
by Jacob Longfloor January 29, 2012