A p-value is the probability of getting a value as extreme as the one observed, given that the null hypothesis is true. This is why you want a low p-value. If you get 0.0004. This mean that IF the null hypothesis is true, then the chance of getting this result is 0.004%, which at that point, you can safely reject the null-hypothesis as probably being untrue, thereby accepting the null hypothesis. Due to the nature of the p-value, if you're doing something like DE analysis or GWAS, then you'll eventually get false positives. Because of this, multiple testing correction must be done.