A fixed effect is “nested within cluster” if the same variable is used in vce(cluster ...) and in absorb(...) or—more generally—if a cluster variable is coarser than a fixed effect variable. For instance, if we have state–clustered standard errors and county–level fixed effects, or with clustering by year and monthly fixed effects.
Whenever this happens, reghdfe will avoid applying a double penalty to the standard errors: it will continue to cluster by e.g. state but will not use the number of counties when computing the absorbed degrees of freedom.
If this option is triggered, you will see the message “fixed effect nested within cluster; treated as redundant for DoF computation” in the second output table of reghdfe