Today it is a method to prevent child searching the web from receiving adult content. Although focused on keeping childern safe, the method can be used on any account.
For this search term, the differences in results include the images shown, total number of results returned, and ordering of the information.
The safe search preference is communicated via the HTTP header "prefer:safe"
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For more information about the header, you can refer to the Internet draft specification submitted to the IETF (Internet Engineering Task Force).
Ultimately, it's up to the website or service owners to honor the safe preference when the browser communicates it to them on the user's behalf, and respond accordingly. We're hoping that more browsers, websites, and services will embrace the standard so that we collectively help build a safer web for our children.