For the most part, YouTube has been pretty good about filtering out inappropriate content, like sexually explicit videos which usually get removed almost immediately after somebody attempts to upload it.
At the same time, sexually explicit content may not be the only type of videos you don't want you your children coming across. This new feature addresses what YouTube has described as,
"potentially objectionable content that you may prefer not to see or don't want others in your family to stumble across while enjoying YouTube. An example of this type of content might be a newsworthy video that contains graphic violence such as a political protest or war coverage."
With the rise of citizen journalism, for example, the Iranian presidential election where one of the primary ways to get news about what was going on was to tune into Twitter to find links to YouTube videos of the violence that was taking place among its citizens. A video of police invading Iranian citizens like this one could be considered disturbing or maybe frightening to a young child.
Either way, it's up to you whether you'd like to turn this filter on. YouTube said the "Safety Mode" link can be found at the bottom of any video page. If you don't see it right now, you'll probably see it by the end of the day as YouTube is stll rolling out the feature.
YouTube admits, "Safety Mode isn't fool proof, but it provides a greater degree of control over your experience."