。
She's furious.
Literal
She [topic-は] very [angry-怒っている].
怒っている is the resulting-state form of 怒る ('to get angry'). 怒る itself can mean either 'become angry' (a momentary event) or 'be angry' (the state); the ~ている form locks in the stative reading: 'is in the angry state.' This is parallel to 知っている ('know'), 持っている ('have'), 結婚している ('be married') — verbs whose ~ている form expresses the resulting state of the change. たいへん intensifies the predicate without changing its nature. A short sentence with a clean grammar lesson: state-result reading of ~ている applied to an emotion verb.