I think it means, like, to understate something. I'm sure if you know what that means, so here are some examples of usage:, "To put it mildy, Hitler was a ......ing sociopath.". Or, "To put it mildly, Bill Gates is really wealthy." However, for some reason, I usually think of this phrase as being used by a person who is commenting on something that another person just said. "Yeah, to put it mildly." Personally though, I never really employ this particular idiomatic phrase. That adjective is for food and weather. I would say, "yeah you think?", or "that's the understatement of the millenia."