This is a correction applied to pValues to take into account the multiple comparisons problem. The correction is computed as:
Corrected pValue = p × k
where:
 p is the pvalue.

k is the correction and is determined by:
 Ranking all the comparisons according to the pvalue, from smallest to largest.
 Computing p × m / i, where:

 m refers to the number of comparisons.
 i refers to the rank order of the pvalues, where the smallest has a value of i of 1, the second smallest has a value of 2, etc.
 Identifying the largest value of i such that p × m / i < α, where α is the Overall significance level. If no values are significant, then we set i = 1, which reduces to the Bonferroni correction.
 Setting k as m / i where i is the largest rank as identified in the previous step.
Note that FDR is actually a method to adjust the cutoffs for significant pvalues; there is no standard way of reporting pvalues corrected by FDR. The pvalues reported in Q differ from the values given in R using p.adjust because R does not set k to a single value. This does not affect the conclusions, but it means that corrected pvalues cannot be compared to each other.
See also
 A worked example of the FDR being applied here.
 Multiple Comparisons (Post Hoc Testing) for a description of how this correction is applied in Q.
 The Multiple Comparisons (Post Hoc Testing) page on Displayr for more information about the theory and practice of correcting for multiple comparisons using the false discovery rate.