The probability that the opposite of some hypothesis is true, based on some set of results; a way of expressing the significance of a statistical observation. The lower the P value, the more significant the result.
For example, if the hypothesis was "This vaccine prevents flu" then the opposite hypothesis (the "null hypothesis") would be "This vaccine has no effect on flu". If the occurence of flu was measured in a sample of people taking the vaccine then one might say that the hypothesis was confirmed with a p value of 5%. That would mean there was a 5% chance of obtaining the same results or better from a similar sample of the whole population even if the vaccine had no effect.