From the (U.S.) National Weather Service’s Weather Service Operations Manual (Chapter C-11, section 8.3.1, if you care):
A POP (probability of precipitation) forecast is the the likelihood of occurrence of a precipitation event at any given point in the forecast area.
A precipitation event is further defined as a measurable amount of liquid precipitation or water equivalent.
So, a “30 percent chance of rain” means that there’s a 30% percent chance of measurable rain (at least one one-hundredth of an inch) at any given point in the forecast area for the length of time of the forecast (usually twelve hours).
It has nothing to do with pattern recognition or past history, as alluded in the article on the web site. Naturally, such pattern recognition or past history may play some part in what number a forecaster will stick in there, but the link stops there.