Let's try a little event history here to make sense of this Russian election hacking accusation. It's not exactly in order, rather it is how the events appear to connect and make sense to me, with lots of speculation on my part.
Hillary Clinton sets up a private email server as Secretary of State, so that she can hide her correspondence from government scrutiny and from becoming part of the public record. This is because it might open her up to future criminal charges if the content of her emails ever became public or were officially investigated.