What does a p-value represent in hypothesis testing?

A p-value quantifies the probability of observing results as extreme as (or more extreme than) those obtained, purely due to random chance, under the assumption that the null hypothesis is true. A conventionally small p-value (commonly <0.05) suggests the result is unlikely to be due to chance alone, supporting rejection of the null hypothesis — but the p-value itself is NOT the probability that the null hypothesis is true, and it doesn't directly measure effect size or clinical importance.