The term “conservative blogosphere” refers to a group of people who have blogs that are written from a conservative point of view. In the last few years, the conservative blogosphere has become much more important than it once was.
The “blogosphere” is the “universe” of people who write blogs. In this case, they are blogs about politics. These people are not really like members of the traditional mass media. They are less likely to report their own stories. Instead, they are providing commentary about things that are happening. They are, in effect, opinion columnists who are self-published rather than writing for some established media outlet. You can see an example of such a blog at this link.
The conservative blogosphere has become more powerful in recent times as there has been a “tea party” inspired backlash against anything that smacks of mainstream thought. The blogosphere is generally rather more radical than the mainstream of the Republican Party. It has helped to pull the party in much more of a conservative direction.
The conservative blogosphere, then, is the group of bloggers who have very conservative points of view.