The text below is taken from Wikipedia article about P-value:
In statistical hypothesis testing, the p-value is the probability of obtaining a result at least as extreme as that obtained, assuming the truth of the null hypothesis that the finding was the result of chance alone. The fact that p-values are based on this assumption is crucial to their correct interpretation.
More technically, the p-value of an observed value tobserved of some random variable T used as a test statistic is the probability that, given that the null hypothesis is true, T will assume a value as or more unfavorable to the null hypothesis as the observed value tobserved. "More unfavorable to the null hypothesis" can in some cases mean greater than, in some cases less than, and in some cases further away from a specified center.