Zapier is a workflow automation software that allows users to create automated workflows called Zaps, which send information from one app to another without coding knowledge required. It enables users to connect their Google Drive account to Dropbox and automatically move Google Doc files from Google Drive to Dropbox by setting up a trigger step in Zapier and an action step in the other direction. The process involves selecting the Google Drive folder where documents will be moved, choosing the Dropbox space and folder for upload, and customizing the file name and extension if needed. Additionally, users can save individual Google Docs files to Dropbox manually by downloading the file from Google Docs and uploading it to Dropbox.