There is a (very brief) account in that post of what decoherence is and why it leads to non-interaction. There is a much more extensive discussion of the point in the previous (linked) post on decoherence.
You do realise that the one-paragraph summary here is only a one-paragraph summary, and that there's a lot more in the original post, yes?
There's not that much more.
There's some claims about how the system evolves, and some more handwaving with Feynman path integrals.
Today's post, On Being Decoherent was originally published on 27 April 2008. A summary (taken from the LW wiki):
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Where Experience Confuses Physicists, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.