The bloggers' web, ie the totality of weblogs and blog-related websites. The term seems to have been coined by William Quick, aka DailyPundit.com, who posted this to his weblog on December 30, 2001:
I PROPOSE A NAME for the intellectual cyberspace we bloggers occupy: the Blogosphere. Simple enough; the root word is logos, from the Greek meaning, variously: In pre-Socratic philosophy, the principle governing the cosmos, the source of this principle, or human reasoning about the cosmos; Among the Sophists, the topics of rational argument or the arguments themselves. (The American Heritage® Dictionary of the English Language)
John Hiler of Microcontent News argues that "while bloggers do often use logic in dissecting arguments, I love the word Blogosphere because it happens to capture another truth: the Blogosphere is a biosphere of its own, a Media Ecosystem that lives and breathes just like any other biological system."
While it's easy to accuse bloggers of sometimes going overboard in metaphorically describing what they do and what blogs are (such as "weblogs are like the salt of the news-soup"), there is something to be said both for the clever blog/logos pun and for the comparison with an ecosystem.
Ambitious as it may seem, the 'logos' part of 'blogosphere' stresses the rational argument side of blogging. Many blogs parttake in debates between bloggers, they comment on each others postings, etc, and, thankfully, it's not all bashing and fisking.
Also, in commenting on each other, linking to each other and making use of their referral logs to see who links to them (and frequently linking back), bloggers form smaller and bigger communities - a lot of them heap up in clusters, having their own discussions and topics going between them. No one sits in any board room organizing this, there is no Blog Editor-in-chief or executive blogging committee deciding who gets to link to whom and should concentrate on what subjects to attract which readers. Which means that the blogosphere is, in most respects, self-organizing.
For those interested in reading about how online communities may function like something out of a biology book, I recommend Steven Johnson's excellent book Emergence (2001) - "The connected lives of ants, brains, cities, and software". At http://www.oreillynet.com/pub/a/network/2002/02/22/johnson.html there is also an interesting interview with the author. (E2 is mentioned in the book, although Johson makes a bigger point out of Slashdot).
Sources:
http://www.dailypundit.com/archives/002327.php#002327
http://www.microcontentnews.com/articles/blogosphere.htm
http://www.leuschke.org/log/archives/week_2002_05_26.html#001730