No, that's not what it is – although that would be ... interesting.
The live analysis board is pretty much like the analysis board that you can access via More -> Game Editor, except that it's located in live chess and you can invite members to chat, watch you analyse, or take control of the board. Read this for all the details:
http://support.chess.com/Knowledgebase/Article/View/160/13/how-do-i-use-the-live-analysis-board
I'm curious about this "live analysis" feature that diamond and platinum members get to use. Can it be used during a game to help a player recognize when their opponent has made a blunder and how to take advantage of it or something like that? If so, me no likey.