Google Analytics' 'site search' reports allows you to see the keywords visitors enter in your website search function. Our company is a Google Analytics Certified Partner and from my perspective as Business Director the new feature not only shows what visitors are looking for on your website but also the importance of having an internal website search function.
Being able to 'see searches' is also invaluable in checking whether the content on your website is sufficient to make it worthwhile to search. If visitors are searching your website and not finding information you want them to have then there is obviously a problem with your content which needs fixing.
If you don't have a website search function you might want to consider setting up Google Site Search which is a hosted solution, which allows people to search within your website.