I am reading a paper that proves the representability for certain functors whose domain is the category of superschemes. The paper claims that to prove representability of functors (or possibly just the functor of interest) in this category we must first place an etale topology on the category.

More broadly, why is this the case? What about certain categories (or functors) requires an etale topology for proving representability problems?

I don't understand the motivation behind this, possibly because I have never really worked with representability problems in much depth.