I think Desmond Rivet wrote a very, very good explanation about the IndieWeb. Here are my favorite pieces from this article:
It’s about control of content, …
When you post a tweet or a status update (or any form of content), it ceases to be yours the second you hit the enter key. What happens to your content if Twitter or Facebook shut down - or, if that seems too unlikely to contemplate, what happens if you simply want to leave?
… silos, …
The IndieWeb community’s blanket term for sites like Facebook and Twitter is silo and the metaphor is apt. People take it for granted that Facebook users don’t get to follow you on Twitter unless they’re also Twitter users. Sending a message to someone on Facebook doesn’t work unless that person is also a Facebook user. You don’t get to comment on Medium articles unless you create yourself a Medium account.
… and how the IndieWeb is trying to make the WWW a social network:
The IndieWeb is an attempt to bring the benefits of social networking […] to the web at large, using open protocols. Whereas a site like Twitter or Facebook is a kind of walled garden, with online social interactions restricted to the confines of the site, the IndieWeb tries to create a social network out of the world wide web itself.
And the reason why the IndieWeb is probably a much better attempt at solving the silo problem than let’s say Diaspora:
A personal website belonging to the IndieWeb doesn’t need to run any particular suite of software, and doesn’t need to be hosted on any particular service. It’s a standard website, written with standard HTML and CSS, using whatever tools you want.