The Advanced search add-on provides category suggestions based on the search query entered by the user.
Search can run using either MySQL or Sphinx. More accurate (relevant) results are delivered with Sphinx, which also suggests keywords and phrases.
Category suggestions are generated from the category name and its dynamic properties.
Suggestions via Sphinx with the setting for listing availability enabled

You can also add extra keywords and phrases in the category settings. This is where you can list common search queries. You can get this kind of statistics using this add-on.
The settings let you choose the search mode and configure suggestions so they take listing availability into account.