Applications for Education
The new search-within-documents option could be useful for students who need to quickly double-check something that they are citing in a research paper. Students who are trying to include a quote that they've heard can take advantage of the "quote search" option that is included in the Google Docs search option.
The new search function doesn't appear to be available to Google Apps users (Google Apps for Edu, Google Apps for Business) yet so you'll have to be in a personal Google account to see the new feature.
To learn more about Google Documents and Google Drive, download my free 57 page guide to Google Drive and Docs for Teachers.