A 'not provided' tip from your Analytics
Why is this?
Key word referrers
Pretty much since search engines have been around website owners have been able to look at their server logs or analytics and see the key words that visitors used in a search to find their site. When a user ran a search in a search engine and clicked on a link, the search term was attached to the URL in the URL referrer.
Some time around November 2011 (based on our internal reports) Google began experimenting with encrypting the search term for logged-in users of Google services, and then rolled it out to the main service in April 2012. What this means is that if you were signed in for Gmail, then ran a search, the website that you visited as a result of that search wouldn't see the key words that you used to find them... all they would see is that you came in from a search, but that the search term was "not provided".
How do marketers cope with the missing key terms?
Most marketers have found this to be exceedingly frustrating, and if you search for answers regarding the "not provided" keywords, you'll find posts written by marketers trying to extrapolate the missing data, or figure out ways to re-craft their campaigns to circumvent this problem. They still won't see the missing information, but their strategies are to still be able to run their campaigns effectively without having that information.
Is there positive insight to be gained?
Rather than be focused on the negative, the information that you're no longer able to see, think about what the information does provide. With a single metric you're now able to see exactly what percentage of your visits come from people that use Google/Gmail accounts and searching while logged in.
You now know that those 30-50% of your search visitors are logged in to Google, and because of this, will be seeing personalized search results. Those search results are easily affected by factors such as past history, localization, and Google's recommendation engine powered by Authorship and G+ socializing. You can compare those statistics against your non-hidden search terms, you can identify what percentage of Google logged-in vs not-in are visiting your site from a search, and you can see how your Google networking has affected your click-thrus coming from logged-in users over time.
That's some pretty interesting insight into the visitors of your site and might give you some thoughts about how to better target them.