"Many users prefer not to have adult sites included in search results (especially if kids use the same computer). Google's SafeSearch screens for sites that contain explicit sexual content and deletes them from your search results. No filter is 100 percent accurate, but SafeSearch should eliminate most inappropriate material."
To lock SafeSearch settings, you'll need to log in using a Google account and select the locking option from the preferences page. "Use this page to lock the SafeSearch settings selected. The lock takes effect when you sign out. when locked, SafeSearch displays a distinctive image as the background of the search results pages," explains Google.
It's not very clear if the locking will be limited to the current browser and whether clearing Google's cookies will disable the lock. Here are some messages that might be used by Google: