As anyone familiar with Google Analytics knows, the platform has kept its keyword data hidden for some time. A number of years ago, it was possible to understand the exact words users searched to find your site, but in 2011, Google began witholding that information, and much of the data became '(not provided)'.
Google claims this was a move towards greater privacy, on the basis that users' website browsing habits are private and personal information. By a happy coincidence for Google, this move encourages web marketers to move towards Google Adwords in order to test out different keywords for clickthroughs and conversions -- but that is a paid service.
There are now a number of ways to unlock (not provided) data. They are all legal, and all give marketers essential insights into where to focus their efforts when optimizing their websites.
1. SEO monitor.
SEO Monitor is a pretty awesome solution to the (not provided) issue. The platform works by aggregating data from Google Search Console (formerly Webmaster Tools) and Google Analytics. Up to 120,000 keywords can be pulled in and analyzed, giving a pretty accurate idea of how people are finding your site, and where you should budget your time and effort in order to increase traffic.
In a recent UK SEO conference, BrightonSEO Rob Kerry gave a talk outlining how PHP can be used to reclaim organic search keyword data. You can have a look at the slides here. This method utilizes already-available code from Google's own API library (basically data that they've made available). Kerry plans to make the code open source some time next month.
3. Your personal on-site search function.
One useful tool for unlocking (not provided) data can be found on Google Analytics itself. If your site has a search function, it's likely that users will be searching on-site for things that they would search for in Google. By properly configuring Google Analytics for site search, you'll be able to understand exactly what users are searching for, allowing you to optimize the site. This is obviously a limited method, since not all users will use the search function of the site, but it's a good way to fill in some blanks for free.
4. Just ask people.
No doubt you're very familiar with marketing pop-ups, fly-ins and email sign-up forms -- the kind that appear when you land on a new page, or are about to leave the site. These nearly always ask for your email address, which is obviously an important piece of marketing data. Perhaps equally important is how the user found your site in the first place. Instead of asking for an email address, ask "What did you search to find this page?" Even a response rate of a few percent should help you better understand your audience's search behavior.
These four methods are all pretty valid ways of getting a good understanding for how people find your website. This understanding will allow you to further optimize the site, learn how people find pages and learn whether they proceed to make an inquiry or a purchase.
There are other methods, but these seem to be the most common-sense for any marketer and are probably the easiest to implement in order to gain the most data.