Anyone familiar with instant messaging / chat programs knows that sometimes it is a nuisance to be "available." While most of your coworkers might know you're on deadline and leave you alone, there's always a few people out there who are desperate to talk about what happened to them over the weekend. They never let you get any work done. Even switching your status to "Busy" or "Please don't bother me" or "Buzz Off!" fails to prevent certain people from reaching out to you. That's the beauty of invisible.
With the new invisible mode in Gmail Chat and Talk, you'll appear offline to your Gmail contacts, as well as to your AIM contacts (if you use AOL's program). You'll be able to see who's online, but they will not be able to see that you are online.
There is, however, a double-edged sword here. If everyone chooses to go invisible, it sort of negates the usefulness of chat programs.
That conundrum aside, you no longer have to worry about Bob down in accounting bothering you about your expense reports when you're busy doing real work.
Now, about Yahoo Instant Messenger...