If you're curious about what Drive is all about, here's an overview: All your changes will automatically be synced across Google Drive and for everyone you've shared that document with - pretty neat. The file would have to be downloaded before it could run on Word with the local Google Drive folder pictured above, that Word file is already on your computer so you can just open it directly, edit and save. Microsoft Word can only run locally, so if you open a Word document in the Web version of Drive you're only able to see a preview of the file.
Most importantly, when you want to open a local file type in Google Drive, you'll want to use the local Google Drive folder.