For some reason GitHub does not display a Follow button on organization pages. So you can only follow normal users or repositories. This is pretty sad because it perfectly makes sense to follow an organization if you want to be informed about new repositories created by this organization. Following the organization members instead isn't an option because then you are also notified about their personal activity which might be boring to you. And some members are not even displayed as organization members because membership can be hidden.
You can also check the follower list of an organization (The link to this list is also hidden on GitHub). Here is an example URL: https://github.com/openwebos/followers. And when you check the Following list of a user which follows an organization then you can even see a Follow/Unfollow button for the organization. This is most likely a bug, GitHub simply forgot to remove this button when they introduced organizations (Which are simply special kinds of users).
Now I wonder: If it is possible to follow organizations and even notifications about new organization repos works then why isn't it an official feature?