I was hoping to dig up a formal thing about the dreamsheep, but all I can gather is that someone drew one, someone thought it was a good idea, and they were quite popular for a while. They're basically the unofficial mascots of Dreamwidth.

He does make a brilliant announcement icon, though I hope I'm not ever doing any announcements like that!

And I suspect a lot of people have an icon or two that has quite the story about it - that one happens to be my big "personal story behind this" icon. :)