A Big Lie is a lie that is so enormous and told so brazenly that most people will to swallow it unthinkingly. Consider the adage:
Tell someone that there are 400 billion stars in the universe and they'll believe you. Tell them a bench has wet paint and they have to touch it.
This is very much the opposite of the skeptical dictum that extraordinary claims demand extraordinary proof.

Hitler is said to have claimed, "the people will more easily swallow a big lie than a small one." But Hitler has become enough of a meme-magnet that I don't know whether to credit any statements of this form.

My favorite example of a Big Lie is the story we've all been told about methylphenidate (Ritalin™).
One would think that a stimulant would make children with ADHD more hyperactive, but due to a paradoxical effect it has on their abnormal nervous systems, it actually calms them down.

The "paradoxical effect" is obvious BS to anyone who has ever taken caffeine to stay up and write a paper, or make a long drive, or code for hours on end. We all know that, in moderate quantities, stimulants make it easier to pay attention. Psychological and physiological evidence from scientific studies invariably back this up. But we have this fear of mind-altering substances beyond the caffeine, nicotine, and alcohol that society officially accepts. So we need to come up with a reason why people who need stimulants to function are "special." Hence the big lie.