I'm sorry if this has to do with my sleepiness, but from that page I don't understand at all what this is. A kind of social CMS? A bloggers community? The page is rich in word count but poor in being informative. I'd be very grateful if somebody could give a little explanation of what this is, because, it seems to be an interesting thing.
IndieWeb is a social movement rather than any one particular technology or project. It's a group of people that believe in publishing as the web was originally intended: a diverse network of participating individuals, not corporations, bound by open standards. There are a number of projects under the general Indieweb banner or just sharing the IndieWeb principles.
The other reply gives a good answer. I'll suggest reading over the about page (https://indieweb.org/IndieWeb:About), I think it's more informative.
Indie web is about people owning their data and having control over it. It's about being able to build what you want for yourself. It's a direction, a set of ideas and principles that some people enjoy.
