So what's the story behind the goat?
Back when Brad was living in the dorms and was also still running FreeVote.com  his roommate Eli and him got bored and decided to make some joke ads to put up on FreeVote.com to advertise LiveJournal.com.
Those original 8 banners, as much as they sucked, are archived for historical reasons at http://www.livejournal.com/banners.bml.
After the first four they'd both run out of ideas and one of them just spouted out, ‘LiveJournal.com... because goats are cool.’ It made no sense, so it was perfect! Then Brad went and found a picture of a goat. That goat then became the unofficial LiveJournal mascot.
So basically, the goat means nothing. But he's so damn cool, and uber sexy.
 FreeVote is currently run by one of Brad's friends.