Many pretentious writers have begun to use the expression “orders of magnitude” without understanding what it means. The concept derives from the scientific notation of very large numbers in which each order of magnitude is ten times the previous one. When the bacteria in a flask have multiplied from some hundreds to some thousands, it is very handy to say that their numbers have increased by an order of magnitude, and when they have increased to some millions, that their numbers have increased by four orders of magnitude.
Number language generally confuses people. Many seem to suppose that a 100% increase must be pretty much the same as an increase by an order of magnitude, but in fact such an increase represents merely a doubling of quantity. A “hundredfold increase” is even bigger: one hundred times as much. If you don’t have a firm grasp on such concepts, it’s best to avoid the expression altogether. After all, “Our audience is ten times as big now as when the show opened” makes the same point more clearly than “Our audience has increased by an order of magnitude.”
Compare with “quantum leap.”