"We wanted to let you know that you have bonus Google Drive storage expiring on Oct 3 2015. While this bonus period is coming to an end, you can always purchase additional storage," informs Google. "Rest assured that your files in Google Drive remain safe and accessible by you and the people you've shared them with. You just won't be able to add or sync any files unless you are using less than your current available storage or you've purchased additional storage."
Basically, Google won't delete your files, but you'll have to delete some of them or purchase more storage if you actually used the 10 GB bonus storage. Since the storage is shared between Gmail, Google Photos and Google Drive, all of these services are affected and you can also delete Gmail messages with large attachments or photos and videos from Google Photos that use your Google storage. Here's how to find Gmail messages with big attachments and a list of Google Drive files sorted by size.