What does "Locked Messages" mean? When I try to delete a message, I get prompted to select whether to "Delete locked messages".

There doesn't appear to be any difference if I check this option or leave it unchecked.

Does anyone know what that means?
You can lock a particular message in your conversation so you don't accidentally delete that. The check box is for those messages. See following screen-shots - 


First Long tap on the message you want to lock, and select Lock.
The message should be now locked and a lock icon should appear at the bottom.
Now when you delete the conversation the message was in, the locked message would not get deleted if the check-box is not selected.