what does the author mean by directory structure in operating system? I'm reading Operating System Concepts by Avi Silberschatz(9thE), in section 11.4 File-System Mounting, the author explains the steps of filesystem mounting as follows:


  
  The operating system is given the
  name of the device and the mount point—the location within the file structure
  where the file system is to be attached.
  Next, the operating system verifies that the device contains a valid file
  system.
  Finally, the operating
  system notes in its directory structure that a file system is mounted at the
  specified mount point.
  


I'm confused with the final step, since to the best of my knowledge, the directory structure is stored somewhere on the disk, which records the files' information -- such as name, location, size, and type. Then what does the author mean by directory structure in operating system? Is it the same directory on disk? 

Additionally, which part finishes the conversion from file name to physical address on disk? Is it the disk driver or the disk controller or done by processor with memory?
Step 3 of that description is indeed a bit confusing, and your comments are right.  The short answer is that the OS keeps track, in memory, of the set of mounted file systems and where they are mounted.