As well as being able to get great information about what people searched on the web to find you (keywords report), Google Analytics can easily be setup to show you what people searched for WITHIN your website.

You just need to tell it some simple information about how your search box works. See here:

Now you can see what people type into your search box and do things like:
Offer new content to match that better;
Have quick links to key information in sidebar & homepage