One possible answer, related to the concept of calibration, is this: it means that it rained in 70% of the cases when you predicted 70% chance of rain.
You've defined your calibration with respect to predicting rain. But I am not interested in calibration, I'm interested in the weather tomorrow. Does the probability of rain tomorrow even exist?
Alternatively, what single concept from statistics would most improve people's interpretations of popular news and daily life events?