For a given real reductive Lie group $G$, we have the notion of a representation being cohomological using the Lie algebra cohomology. In particular we know that the discrete series representations of $G$(whenever it exists) is cohomological. I am trying to understand what information do we exactly obtain when we know that these representations are cohomological. Also, why are cohomological representations important and what role do they play in the global setting, i.e in the setting of automorphic representations?
It would be great even if you could direct me to an appropriate reference. Thanks in advance.