I am not sure I would call it "particularly" safe. I would say it is a lot safer than North Beach or areas around the Tenderloin and south of Market. But you are still in SF, which like any other major metropolitan city is more dangerous the burbs. For example, in the last week there have been a half dozen assaults reported in the Russian Hill area (as opposed to three times that number in neighboring North Beach).
In other words, if you use common sense you should be okay. Don't go out late at night, alone. Pay attention to where you are. And be prepared for the occasional auto break-in if you don't have a garage.
Russian Hill is a very safe area. As long as you use your common sense you should be fine. Don't walk around late at night alone, and don't be silly towards other people. Same rules apply in most neighborhoods in San Francisco.