In this day and age, parents are expected to take up more of an active parenting role for their children than was previously expected of them decades ago. You can thank technology and a gradual liberalization of society for that. In the days of your parents' childhood, the most your grandparents probably did was monitor the television programs and movies they were watching, and probably keeping a close eye on who they were calling on the family telephone.
Nowadays, children have the entire world at hand via the family computer, or their own computer. The Internet's an uncensored free-for-all with lots of undesirable content available, and undesirable eyes watching. "Net nanny" software can block off the former, but not necessarily the latter - and that's where good parenting fills in the void. A common tactic for parents would be demanding their children to tell them their passwords for all their accounts, just so no questionable communications are had.
What if they refuse to comply? Option one: bring out the wooden stick! (Oh wait. That's illegal now.) Option two: hold their electronics hostage until they comply. Or, you can thank Facebook if they happen to have an account there: a third option is to simply contact Facebook and demand certain edits be made to your liking. That is, if you live in California and this California bill goes through.
As reported on TechCrunch, this bill will force social networks to allow parents the ability to manipulate parts of their children's profiles, which includes changing their privacy settings to the highest level, and requesting specific text or pictures to be removed. If social networks do not comply with the request within 48 hours, they could be hit with a $10,000 fine per case.
The original version of the bill would have also made it illegal for any minor to post their home address or telephone number anywhere on a social networking site regardless of privacy settings. Expecting minors to not be able to share their own cell phone number with friends is a bit silly, and so the revised bill has dropped the age requirement, but still allows parents to request removal of this information.
While it's nice to give some parenting control back to the parents, it does create some serious consequences. What if divorced parents could wage "war" over their children and manipulate their pages to their liking? How do the parents prove to Facebook that they are indeed the parents of who they claim their children to be, without requiring too much personal information to be handed over? Facebook has already been known to act first before taking evidence into consideration.