Visibility options let you control how people access your files, folders, and Google Docs. Anything that you create, sync or upload in Google Drive starts out as private.
When you create a private doc, you're the only person with access to it. From there, you can give access to other people. Anyone trying to access the document will have to sign in to their Google Account to verify that they have access to the doc.
Something set to Anyone with the link is like an unlisted phone number. Another person can only view it if they have the exact URL of the doc, file or folder. If you also select the "Allow anyone to edit" option, anyone with the link will also be able to edit your doc. Since sign in isn't required, viewers and editors may show up as anonymous.
Choose Public if you want something to be available to anyone. Public documents and files can show up in search results, and anyone who finds the web address of the doc can access it. If you also select the 'Allow anyone to comment' and/or 'Allow anyone to edit' options, anyone who finds the document will also be able to view, comment and edit your document.
If you're a Google Apps customer, your domain's default setting might be different, but you can change the visibility level to Anyone with the link or Public on the web if you’d like to give access to more people.
Google Apps users also have the option to make documents public only to users on their domain. Selecting a domain name — say, "Example.com" — as a visibility option means that users on that domain can find the file by using the "Search [that domain]" option in the Advanced Search menu. When the Anyone at Blake School with the link option is selected, the file won't appear in "Search [that domain]" results.
Reference: Google - Help - Sharing settings overview