The definition
In statistics, a p‑value is the probability of obtaining a result at least as extreme as the one actually observed, assuming the null hypothesis is true.
The null hypothesis is the boring explanation — that there is no effect, no difference, nothing but chance. A small p‑value means the observed data would be unlikely under that boring explanation, which counts as evidence against it. A large p‑value means the data is perfectly consistent with nothing happening.
Where 0.05 comes from
By long-standing convention the threshold is α = 0.05: a result with p < 0.05 is called statistically significant.
The threshold is a convention, not a law of nature. It was popularised by Ronald Fisher in the 1920s, and the specific choice of 0.05 is arbitrary. Different fields use different thresholds for good reasons — particle physics demands far stricter evidence than a usability study does.
Three things a p‑value is not
It is not the probability that the hypothesis is true.
It is not the probability that the result happened by chance.
It is not a measure of effect size. A tiny, practically useless difference can produce a very small p‑value given a large enough sample.