What the IGF is
In a nutshell, the Tunis Agenda by which the IGF was founded states that it is means to be a "new forum for multi-stakeholder policy dialogue." The background behind it is that it was acknowledged at WSIS (the summit at which the Tunis Agenda was drafted) that no single country, and for that matter no single stakeholder group (eg. governments), was entitled to govern the Internet on its own.
So the IGF was a place for all of the stakeholder groups to come together to work out the appropriate public policy responses to problems of Internet governance. Because it had no binding authority, its views were only to have the status of recommendations.
However, some parties are now trying to weasel out of the deal reached at WSIS so that even the power to make recommendations is taken away from the IGF. This is why you had trouble understanding the IGF's role based on discussions at the ICANN meeting.
For more background, see http://igfwatch.org.