The change should fix an annoying issue in Drive that can prevent users from downloading files if third-party cookies are disabled. If you encounter the problem, the advice from this Google support page is to manually create an exception for Google Drive to allow third-party cookies.
Google’s blog post does not explain why Google Drive currently relies on third-party cookies, but there is speculation that this is because the service uses a separate domain (googleusercontent.com) to host the content uploaded by users as a security measure. Cookies are then used to verify that you have permission to download a given file. We’ve contacted Google to ask about this and will update this article with any response.