Of every person told this quote, they tell it to > 1 other new person on average.

So the "r" stands for what, repeatability? Where did this jargon originate (and more importantly, why do web searches only turn up insulation values)?

For a virus, the average number of people a sick person infects. If r < 1, the spread is self-limiting. If r > 1, it spreads exponentially until r drops (because, say, enough people develop immunity).