This happens if, when you made the backup, you had multiple files listed in the backup destination textbox. Go back to your source server and create the backup again; this time, make sure there’s only one destination file listed.
If you had more than one file listed as the backup destination, the backup is striped across them; you’ll need all the files to perform the restore.
You can verify this by performing a RESTORE LABELONLY against the single file you copied to your destination server.