What could you do with this data? Find out what users content they want, how they phrase their terms, what content is missing. Also analyze from where and when they used the search bar, it could provide some clues on what they’re looking for.
[Analyzing search logs right on one's site is a an easy way to understand what users are looking for]
Yes another way to evaluate the user experience. Louis Rosenfeld has a speech, research, and a book on the same topic.