Used to describe a person being an idiot / being incredibly silly and stubborn. Originating from the billy goat itself, because of its outward ridiculous appearance (big horns and a beard... You be the judge) and because of their mating habbits. Two males fighting over a female will run at each other and butt heads to impress the female, which really, is a stupid way to go about it.
Literally: Somebody who goes around and headbutts people.
Rodney is one crazy fucker, who will do anything for a laugh. Always acting the billygoat, that one.
Tom: What's wrong? And what's with the bruise on your forehead?
Jane: Jack. He loves acting the billygoat... Especially in bed.
Tom: Now, that was too much information.