But what is a permissions fix and why is it needed? What if you don't do such a fix, then what will happen? (why is the fix not built into the Time Machine restore?)
The permissions fix is to Open Disk Utility, select your boot disk and run the Repair Disk Permissions
What this does is compare the permissions of the files and directories installed by Apple to what is expected and changes them if needed.
If you have just installed OSX and then installed from a good backup then all the files will have the correct permissions and will not change anything. So it is a step that is a double check and probably not required but might find something on odd occasions. I would not run this as if there was a difference between expected and actual permissions I would want to know what it is and work out what action broke the set up and fix that error and fix that action.