Micro.blog is a “social network” built on top of the open web and the indieweb. This means that most of it is decentralized. With a few noteable exceptions. This blog post is intended to be a short summary of how it all ties together.
When you register a user at Micro.blog you get a @-username, by default you also get a username.micro.blog site, if you chose to you can continue to use this as your micro.blog if you want to or you can set up your own web site somewhere else.
All posts lives in your own site, while replies lives on Micro.blog. The only thing your site needs to have is a RSS or JSON feed that you add to your Micro.blog user. I have three sites connected to mine.
Then, if you wish to use the Micro.blog apps to update your site it either have to support Micropub or MetaWeblogAPI.