There are several possible reasons probably hindering you from writing files to the USB drive, such as connection failure, account user permission, file system incompatibility, and drive failure.
If the drive is poorly connected to your computer, it is quite normal that it refuses your writing action. For a solid connection, please make sure the drive is connected firmly to the computer port. If a cable or adapter is applied, check if it works well.
Suppose that you are limited to read-only on the USB drive, you're not allowed to write files to it. You can go to Get Info and scroll to the Sharing & Permissions tab, then change the account user's permission to Read & Write.
If your USB drive is formatted to an incompatible file system like NTFS, it will block away your writing move undoubtedly. Trapped in this, you can either apply iBoysoft NTFS for Mac or format the drive to a compatible file system.
Concerning the drive failure, it certainly is unwritable or unreadable. The final thing you can do is give data recovery a shot and purchase a new drive for storage purposes.