While this is really a statistics question, this concept is used often enough in bioinformatics that it's still topical (IMHO).

Let's suppose we wanted to waste some money and took liver samples from 20 wild-type mice and sent them out for RNAseq. We then aligned/etc. the data and randomly divided the results into 2 groups of 10 samples (don't ask why, this is a made-up example). We then used DESeq2 or edgeR or pretty much anything else to compare these two artificially created groups. Since we don't expect there to be any real difference between the artificial groups, what do we expect the raw p-values to look like? Well, we expect ~5% of them to be <=0.05, ~10% to be <= 0.1, and so on. Why, because that's one of the definitions of a p-value (we'll use frequentist definitions, because that's appropriate here). In short, a p-value of 0.05 says that you should see an effect size of this magnitude or greater 5% of the time if the null hypothesis is actually true.

Knowing that, if we see p-values following a uniform (i.e., a flat histogram) distribution, then odds are good that we didn't find much different between the groups. If there's an enrichment in low p-values, then there's probably something interesting in the results. This then leads to how Benjamini-Hochberg p-value adjustment works (using the graphical method). In short, you order your p-values and then plot them versus their rank in the order. You then superimpose a straight line on top of this. Any points below the line are significant (apparently there's an example of this in the TeachingDemos CRAN package).

Edit: People sometimes run into the case where there's actually a depletion of p-values in the 0-0.05 range or a significant slant from lower left or to upper right in the p-value histogram and wonder what that's about. The common cause of this is a batch effect or some other variable that's not being properly controlled.