Why RR cohomology is important in string theory?

I want to know the RR cohomology in string theory or topological field theory in detail. (RR stands for Ramond Ramond). In following papers they compute the nilpotency of differential operator for RR fields. I know for example, from BRST symmetry, cohomology is important (in some sense?).

I want to know why some people compute RR cohomology [what is important in computing RR cohomology?, what is physics behind RR cohomology? ..]

Followings are some papers related with RR cohomology on the arxiv.

First of all i know the terminology cohomology, homology from my topology classes. Also i am somehow familiar with computing nilpotency of differential operators. But during the computation i came up with why RR cohomology is important in string theory, so i make a question here.