It looks like the iMovie app lost its link to the library. If your library is on an external drive make sure that the drive didn't get unplugged. I don't know whether your project is corrupted. You can look in the iMovie backups folder to see if you can find your project.
To get to the iMovie Backups folder, follow this file path from the Finder menu:
Go/Home/Library/Containers/com.apple.iMovieApp/Data/Library/Caches/iMovieBackups
When you get there you will see a list of previous backups of your iMovie library. Click on one dated just before your issue started. iMovie will open in that library. Navigate to your projects browser (where your projects are displayed as icons) and see if your projects are intact.
If the above is unsuccessful, try shutting down your computer and then rebooting. See if that restores the link.
If no luck, try booting up in safe mode. (See Finder help for instructions.)
If still no luck, try deleting preferences by opening iMovie while holding down the Option and Command keys and selecting to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your projects. Now see if the issue is resolved.
If Safe Mode and deleting preferences do not solve it, try redownloading iMovie. To update/redownload iMovie 10, drag your iMovie 10 app from the Applications folder into the trash, but do not empty the trash. Sign in to the app store and open your purchases folder by clicking on your name at the bottom of the app store side bar. You will see your purchases displayed, including iMovie 10. Redownload/update iMovie from there. If not successful, drag your present iMovie app out of the trash and return it to the Applications folder.
-- Rich