A false discovery rate (FDR) is a methodology that can be useful when struggling with the problem of multiple comparisons.
In any experiment, if the experimenter checks more than one dependent variable, then they are making multiple comparisons. Naturally, if you make enough comparisons, you will eventually find some correlation.
Classically, people applied the Bonferroni Correction. In essence, this procedure dictates that you should lower your p-value (raise your standard of evidence) by a specific amount depending on the number of variables you're considering. While effective, this methodology is strict about preventing false positives (type i errors). You aren't likely to find evidence for a hypothesis that is actually false using Bonferroni. However, your exuberance to avoid type i errors may have introduced some type ii errors. There could be some hypotheses that are actually true, which you did not notice.
This episode covers an alternative known as false discovery rates. The essence of this method is to make more specific adjustments to your expectation of what p-value is sufficient evidence.