Furious, apoplectic, absolutely beside oneself with rage. (Imagine a rabid dog, foaming at the mouth and - wait for it! - barking...)

Can also refer to someone who is unbalanced (using "mad" in the British sense, referring to an insane person).

(UK Usage) - Almost Insane, usually in a socially acceptable manner. Often used to describe the behaviour expected of some (rural) old money families and more a likable eccentricity than a true mental disfunction.