A Bonferroni correction is a calculation intended to reduce the likelihood of a false positive in study results by accounting for a high number of comparisons — high enough that it could lead to a statistically significant result simply because of how many comparisons are made.
Deeper dive
As described in the key concept of P-hacking, if the data from a study are examined in enough different ways, some kind of association will usually emerge, based purely on the statistical chance that you’ll find something if you look hard enough in enough different places. If you’re only comparing four things, a statistically significant result is likely a true effect. But if you’re comparing 30 different exposures, you would expect to find associations between some of them simply because the chances of a random association increase as the number of comparisons increases. The Bonferroni correction is a statistical adjustment that’s intended to offset this possibility by establishing a lower threshold for statistical significance.
The mathematical mechanics of it (described here and here) aren’t important so much as simply understanding that it exists for two reasons. First, you might come across it in a study’s methods, which tells you that the researchers are aware of how many different outcome possibilities might be in their paper and they want to be sure none of them result from statistical chance. Second, you want to note the absence of Bonferroni correction if you’re reading a study that seems to have a lot of possible outcomes (and/or sub-analyses), but the authors don’t note any attempts to control for statistically significant results that emerge by chance. Having multiple dependent or independent variables or statistical tests conducted on a single data set is a situation where a Bonferroni correction should be used to ensure the results are “real.”