I need to keep this one in mind for explaining P values to folks. From Skeptoid, an episode about King Tut’s Curse, of all things:

To better understand these results, it’s necessary to comprehend what’s meant by a “p-value”.It’s a term used by statisticians, and it refers to the probability that your test results could be due to normal random variations. A p-value of 0, the lowest possible, means there’s a 0% chance that your test results are due to normal random variances, so low p-values generally mean that your results are significant. A p-value of 1, the highest possible, means that your results are 100% consistent with what we’d expect to see from normal random variations, therefore your results are quite probably insignificant.Of 44 Westerners present, 25 were exposed to the curse. Those 25 lived to an average age of 70, while those not exposed lived to 75. The p-value of this difference was .87, so there’s an 87% chance that this difference was merely due to chance. Average survival after the date of exposure was 20.8 years for the exposed group, and 28.9 years for the unexposed group. While this sounds like a large difference, the p-value was .95, meaning there’s a 95% chance that you’d have such a difference anyway due to random variation. Nelson’s conclusion: “There was no significant association between exposure to the mummy’s curse and survival and thus no evidence to support the existence of a mummy’s curse.”

Emphasis mine, to denote nerdiness. 🙂