So as to not get detected that you are online. Nobody except admin will be able to view what you are viewing. Goto anybody's profile and it shows you what that person is currently viewing. (if he is online) In invisible mode you can stop other people from letting them know that you are online and what are you viewing on the forums.
Why will anyone want to be not visible on an site? Is it cool?
Because they don't want other people to know what they're doing. It's called privacy
Cuz
this two stalk'ye...
#PS: Thanks Bositman.
LOL KrossX, you meanie. 
they want to be silent as ninjas :-)
The same topic came up on the Blizzard forums just recently again.
I don't get why privacy is such an issue with the latest games.
Why is it so hard to give people the possibility to play their bought games without
the whole world knowing they are online (and thus available for chat or co-op play or whatever)?
I realize this here is about a forum feature but the problem is the same.
Afraid from being bugged while playing maybe?
i always get bugged while playing because of Skype. lol